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Here, the authors correct the proof in the reference when explaining that the produced plateaued functions have no non-zero linear structures. Moreover, a new class of plateaued functions with the best algebraic degree is given.

In order to diagnose the wind turbine rolling bearing faults with vibration signals effectively, a fault diagnosis method based on Hankel tensor decomposition is proposed. Firstly, IMF-SVD (intrinsic mode function, IMF; singular value decomposition, SVD) is used to estimate the number of sources in sensor observation signals. Secondary, a third-order Hankel tensor is formed by the observation matrix, and a set of low-rank tensor subterms are obtained by tensor rank- decomposition. The fault features of each source are contained in the first and second modes of the corresponding subterm. Then, the source signals are reconstructed by the subterms. Finally, the envelope spectra of the reconstructed source signals are analysed, and the fault characteristic frequencies are extracted. The results of simulation and practical case analysis show that this method can realise the fault diagnosis of wind turbine rolling bearings correctly and effectively.

The structural characteristics and modes of the Stewart platform driven by electric cylinders are briefly introduced. Based on Simulink, the modelling method of the platform is analysed. To obtain the coordinate transformation of Stewart platform, the rotation matrix and homogeneous transformation are resolved, and the mathematical model of the electric-driven Stewart platform is established related to the structural characteristics. The simulation model of input and output signals is constructed by using graphical user interface (GUI) module provided by Simulink. The motion simulation curves of six electric actuators under different position and posture are obtained, which gives benefit to understand and control the different motion states of the electric-driven Stewart platform.

For improved discrimination of a ballistic warhead from a decoy, a simple 3D feature vector (3DFV) is proposed that is composed of the fundamental frequency, the bandwidth, and the sinusoidal moment of the time–frequency image. Compared to two existing methods, the 3DFV was more efficient and gave results that were less sensitive to noise.

A new characterization of balanced rotation symmetric (*n*, *m*)-functions is presented. Based on the characterization, the nonexistence of balanced rotation symmetric (*p* ^{ r }, *m*)-functions is determined, where *p* is an odd prime and *m* ≥ 2. And there exist balanced rotation symmetric (2^{ r }, *m*)-functions for 2 ≤ *m* ≤ 2^{ r } − *r*. With the help of these results, we also prove that there exist rotation symmetric resilient (2^{ r }, *m*)-functions for 2 ≤ *m* ≤ 2^{ r } − *r* − 1.

In recent years, two new types of irreducible pentanomials, i.e. Type C.1 and Type C.2 pentanomials, and their associated generalised polynomials bases (GPBs) have been proposed to yield efficient bit-parallel multiplier architectures. The GPB squarer for Type C.1 pentanomial is also investigated previously. But no GPB squarer for Type C.2 pentanomial is given as these pentanomials are far more complicated. In this Letter, the authors give explicit GPB squarer formulae for all Type C.2 pentanomials by re-classifying these pentanomials into certain sub-groups, which is based on the parities of pentanomial parameters. As the main contribution of this Letter, the authors show that the GPB squarers for most Type C.2 pentanomials match the fastest results.

In this study, a delay-dependent memory state-feedback controller for linear systems with input time-delay in the presence of external disturbance has been investigated. At first, a new formula is introduced to obtain the prediction vector from the system dynamics and then by using this formula, the effect of input time-delay on the original delayed system is reduced. To guarantee the prescribed disturbance attenuation level of the closed-loop system, Lyapunov theory and linear matrix inequality (LMI) approaches are used. In the case of feasibility, sufficient LMI conditions provide the stabilising gain of the predictor-based controller. To illustrate the effectiveness of the proposed method, it is applied to a quarter-car model of an active suspension system considering the actuator time-delay.

Using the linear representation of symmetric group in the structure vector of finite games as its representation space, the inside structures of several kinds of symmetric games are investigated. First of all, the symmetry, described as the action of symmetric group on payoff functions, is converted to the product of permutation matrices with structure vectors of payoff functions. Second, in the light of the linear representation of the symmetric group in structure vectors, the algebraic conditions for the ordinary, weighted, renaming and name-irrelevant symmetries are obtained as the invariance under the corresponding linear representations. The semi-tensor product of matrices is a fundamental tool in this approach.

Toeplitz matrix–vector product (TMVP) decomposition is an important approach for designing and implementing subquadratic multiplier. In this Letter, a symmetric matrix (SM), which is the sum of a symmetric TM and Hankel matrix, is proposed. Applying the symmetry property, 2-way, 3-way and *n*-way splitting methods of SMVP is presented. On the basis of 2-way splitting method, the recursive formula of SMVP is presented. Using the two cases *n* = 4 and 8, the SMVP decomposition approach has less space complexity than 2-way TMVP, TMVP block recombination and symmetric TMVP for even-type Gaussian normal basis multiplication.

The right and left con-Sylvester matrices for two polynomials are defined, and then the criteria for right and left coprimeness of two polynomials in the framework of conjugate product are given in terms of the determinant of the right and left con-Sylvester matrices, respectively. The results in this study can be viewed as a generalisation of the well-known Sylvester resultant criterion for coprimeness of two polynomials in the framework of ordinary product.

The manufacturing cell design problem (MCDP) aims to minimise the movements of parts between the production cells. The MCDP is an NP-Hard optimisation problem with a binary domain. For the resolution of the MCDP, the authors employ the firefly algorithm (FA) metaheuristic. FA is a metaheuristic with a real domain; therefore, an efficient method for transfer and discretisation from the real domain to the binary domain has been used. The second metaheuristic used is Egyptian vulture optimisation algorithm (EVOA). EVOA is a recent metaheuristic inspired by the behaviour of the Egyptian vulture bird. EVOA uses a set of operators which must be adapted to the MCDP optimisation problem. Two types of experiments have been performed. The first experiment consists of solving the MCDP with a set of 90 homogeneous incidence matrices. In the tests, FA and EVOA have been used obtaining good results. Subsequently, the obtained results have been compared versus other eight metaheuristics. The second experiment consists in a set of 35 inhomogeneous incidence matrices. The global optimum value for 13 problems has been obtained using constraint programming. Finally, for the other 22 problems, the authors have reported the best values found using FA and EVOA.

This study investigates the periodic event-triggered control for the hand position centroid consensus/formation problems of multiple non-holonomic wheeled mobile robots. By constructing invertible input transformation, the dynamics of the hand positions are formulated as two groups of first-order integrators. Then, the event-triggered control laws and the event conditions are proposed. On the basis of Lyapunov theory and the algebraic graph theory, permissible value ranges of the sampling period and the event condition parameters are established, guaranteeing that all the hand positions asymptotically tend to the common initial centroid location or the desired formation shape centred at the initial centroid. In addition, the orientations and the velocity inputs of each robot are ensured to reach some constants and zeros, respectively. Finally, simulations illustrate the efficiency of the proposed theoretical results.

This study is concerned with the finite-horizon bounded synchronisation and state estimation for the discrete-time complex networks with missing measurements based on the local performance analysis. First, a new local description of the bounded synchronisation performance index is proposed, which considers only the synchronisation errors among neighbours. In addition, a more general sector-bounded condition is presented, where the parameter matrices are different for different node. Next, by establishing the vector dissipativity-like for the complex network dynamics, the synchronisation criterion is derived in term of the locally coupled conditions for each node. These conditions implemented in a cooperative manner can judge whether the complex network reaches synchronisation. Similarly, the existence conditions for the estimator on each node are obtained, and then the estimator parameters are designed via the recursive linear matrix inequalities. Notably, these conditions on each node by cooperation among neighbours can achieve the desirable performance index. The distinctive features of the authors' algorithms are low complexity, scalability, and distributed execution. At last, two numerical examples are utilised to verify the effectiveness and applicability of the proposed algorithms.

The positive fraction vector fitting (PFVF) is a special method to guarantee the passivity of rational models such as frequency-dependent network equivalents. It involves constraints that enforce each fraction of the rational model to be passive, which are much stricter than the original passive requirements. PFVF lacks theoretical foundation but works well in practise. This study explains the rationality of PFVF by revealing important features of rational models that the complex-pole fractions corresponding to dominant resonance peaks can be adjusted passive through a minor change. The numerical case corroborates the theoretical analysis.

Sequential order one negative exponential (SOONE) function is used to measure the sparsity of a two-dimensional (2D) signal. A 2D gradient projection (GP) method is developed to solve the SOONE function and thus the 2D-GP-SOONE algorithm is proposed. The algorithm can solve the sparse recovery of 2D signals directly. Theoretical analysis and simulation results show that the 2D-GP-SOONE algorithm has a better performance compared with the 2D smoothed L0 algorithm. Simulation results also show that the proposed algorithm has a better performance and requires less computation time than 2D iterative adaptive approach.

This appendix contains a short overview of the concept of vectors and linear transformations (dyadics) of vectors, and how these are represented in terms of their components. Transformations between different rotated coordinate systems are also reviewed as well as the corresponding transformation of the components of a dyadic. The appendix ends with a short overview of quaternions and their use to represent rotations.

The synthesis of optimal controllers for vibrational protection of large-scale structures with multiple actuation devices and partial state information is a challenging problem. In this study, the authors present a design strategy that allows computing this kind of controllers by using standard linear matrix inequality optimisation tools. To illustrate the main elements of the new approach, a five-story structure equipped with two interstory actuation devices and subjected to a seismic disturbance is considered. For this control setup, three different controllers are designed: an ideal state-feedback *H* _{∞} controller with full access to the complete state information and two static output-feedback *H* _{∞} controllers with restricted neighbouring state information. To assess the performance of the proposed controllers, the corresponding frequency responses are investigated and a proper set of numerical simulations are conducted, using the full scale North-South El Centro 1940 seismic record as ground acceleration input. The obtained results indicate that, despite the severe information constraints, the proposed static output-feedback controllers attain a level of seismic protection that is very similar to that achieved by the ideal state-feedback controller with complete state information.

A novel approach to fuel–air ratio (FAR) control for spark ignition (SI) engines is presented in this study. The FAR dynamics are modelled as a first-order plus time-varying delay system. Time delay in the control plant is not approximated using the Pade formula. For controller design purposes, it is described as a time-varying delay in the measurement output. A gain-scheduled delay-dependent controller, regarding the time delay as a time-varying parameter, is then designed to track FAR reference and minimise the effects of disturbances on FAR regulation. The proposed controller guarantees the stability of closed-loop system and induced *L* _{2} norm performance using Lyapunov–Krasovskii functional. The design method is then formulated in terms of linear matrix inequalities that leads to a convex optimisation problem and can be solved by parameter gridding technique. Simulation results validate the FAR regulation of proposed controller over the large range of time delay, which covers most engine operating conditions in practice.

In this chapter, we consider the representation of vector functions (often referred to as “vector fields”) with low-order (constant and linear) polynomial basis functions on simple cells, such as triangles or quadrilateral cells in two dimensions or tetrahedrons and bricks in three dimensions. As will soon be apparent, there are multiple ways of defining vector basis functions, and therefore the approach requires some consideration. The proper representation of a function depends on what will be done with it-do we need to compute the curl of the function, for instance? If so, the representation might be different than if we need to compute the divergence of the function. We use the term curl conforming to denote the space of vector functions that maintain first-order tangential-vector continuity throughout the domain and can be differentiated via the curl operation, without producing unbounded or generalized functions (Dirac delta functions) in the process. The term divergence conforming is used to denote the complementary space of vector functions that maintain first-order normal-vector continuity throughout the domain and can therefore be differentiated via the divergence operation. (First order or C_{0} continuity is continuity of the function itself, but not necessarily continuity of its first derivatives.) The simple low-order polynomial vector basis functions in widespread use are either curl conforming or divergence conforming; seldom we will use functions that maintain complete continuity and belong to both the curl-conforming and divergence-conforming spaces, although it is possible to define such functions.

Owing to their complexity, accurate and detailed models of anaerobic digestion cannot be used for online monitoring and control. To this aim reduced order models have to be considered. In this chapter, a modification of the well-known AMOCO model is first proposed in order to widen its field of applicability. Then, to perform parameter identification, a linear fractional transformation (LFT) formulation is derived, thanks to the use of a symbolic manipulation tool applied to an object-oriented model formulation. The approach has been applied to two case tests: in the first test, the data used for identification have been generated by a simulation of the fully detailed Anaerobic Digestion Model no. 1 (ADM1) model, assuming waste activated sludge as influent substrate, and in the second, the data have been collected on a real plant, used for anaerobic digestion of agricultural wastes.

This paper describes an efficient implementation of a form of linear semi-infinite programming (LSIP). We look at maximizing (minimizing) a linear function over a set of constraints formed by positive trigonometric polynomials. Previous studies about LSIP are formulated using semi-definite programming (SDP), this is typically done by using the Kalman Yakubovich Popov (KYP) lemma or using a trace operation involving a Grammian matrix, which can be computationally expensive. The proposed algorithm is based on simplex method that directly solves the LSIP without any parameterization. Numerical results show that the proposed LISP algorithm is significantly more efficient than existing SDP solvers using KYP lemma and Grammian matrix, in both execution time and memory.

Given a graph G = (V, E) with a set W ⊆ V of vertices, we enumerate colorings to W such that for every two enumerated colorings c and c' the corresponding colored graphs (G, c) and (G, c') are not isomorphic. This problem has an important application in the study of isomers of chemical graphs such as generation of benzen isomers from a tree-like chemical graph structure. The number of such colorings can be computed efficiently based on Polya's theorem. However, enumerating each from the set of these colorings without using a large space is a challenging problem in general. In this paper, we propose a method for enumerating these colorings when the automorphisms of G are determined by two axial symmetries, and show that our algorithm can be implemented to run in polynomial delay and polynomial space.

Word search is a classical puzzle to search for all given words on a given assignment of letters to a rectangular grid (matrix). This problem is clearly in P. The inverse of this problem is more difficult, which asks to assign letters in a given alphabet to a matrix of given size so that every word in a given wordset can be found horizontally, vertically, or diagonally. This problem is in NP; it admits a trivial polynomial-size certificate. We prove its NP-hardness. It turns out to be so even under the following restrictions: 1) the alphabet size is 2 (binary) and 2) all the words to be found are of length at most 2. These results are optimal in the sense that decreasing these bounds 2 to 1 makes the problem be trivially in P.

Polynomial parahermitian matrices can accurately and elegantly capture the space-time covariance in broadband array problems. To factorise such matrices, a number of polynomial EVD (PEVD) algorithms have been suggested. At every step, these algorithms move various amounts of off-diagonal energy onto the diagonal, to eventually reach an approximate diagonalisation. In practical experiments, we have found that the relative performance of these algorithms depends quite significantly on the type of parahermitian matrix that is to be factorised. This paper aims to explore this performance space, and to provide some insight into the characteristics of PEVD algorithms.

This paper presents a flexure pressure sensor fabricated by means of 3D printing. This sensor combined with a biosimulant artifact from the National Institute of Standards and Technology (NIST) is used to measure the severity of injuries caused in the case of a robot impact with a human. The stiffness matrix is derived for the structure by means of screw theory. A Finite Element (FE) model is constructed to verify the analytical model and obtain the allowable pressure with regard to the yield stress.

According to the characteristics of a new type of complex joint in the space steel structure, one model of automatic assembly system with 6-DOF was designed. Base on Denavit-Hartenberg method and matrix inverse operation principle, the positive and forward kinematics algorithm of an assembly machine is proposed and the main parameters of pose algorithm are calculated. The automatic assembly machine was designed, and its structure and principle of operation strategy was elaborated.By the control method of point to point, experimental data are obtained and then are compared with the theoretical data. The results show that this pose algorithm and its assembly control strategy is available. The maximum deviation of the rotating joint is 0.11 degrees and the maximum deviation of transfer joint is 0.1mm, which can meet the assembly demand in practice.

This study deals with the design of a robust fault estimation and fault-tolerant control for vehicle lateral dynamics subject to external disturbance and unknown sensor faults. Firstly, a descriptor state and fault observer is designed to achieve the system state and sensor fault estimates simultaneously. Secondly, based on the information of on-line fault estimates, a robust fault-tolerant controller based on static output-feedback controller (SOFC) design approach is developed. To provide linear matrix inequalities of less conservatism, the results are conducted in the non-quadratic framework dealing with unmeasurable premise variables case. Simulation results show the effectiveness of the proposed control approach when the vehicle road adhesion conditions change and the sideslip angle is unavailable for measurement.

This study considers the pinning synchronisation in a network of coupled Lur’e dynamical systems under directed topology. By using tools from M-matrix theory, S-procedure and Lyapunov functional method, some simple pinning criteria in terms of linear matrix inequalities, whose dimensions are just determined by the size of a single Lur’e node, are derived for Lur’e networks with fixed and designed inner coupling matrices, respectively. A selective pinning scheme is proposed for a directed Lur’e network such that the network can be globally asymptotically pinned to a homogeneous state. Simulation results are provided to illustrate the effectiveness of the theoretical analysis.

We consider the computation of r-th roots in finite field-s. For the computation of square roots, there are two typical probabilistic methods: the Tonelli-Shanks method and the Cipolla-Lehmer method. The former method can be extended to the case of r-th roots, which is called the Adleman-Manders-Miller(AMM) method. The latter method had been generalized to the case of r-th roots with r prime. In this paper, we extend the Cipolla-Lehmer to the case of r-th root with r prime power and give the expected running time of our algorithm.

This chapter designs a non-fragile H_{∞} controller for a class of active suspension systems with actuator uncertainty. By using Lyapunov stability theory, a nonfragile controller is designed for the purpose of ensuring that the resulting active suspension system is asymptotically stable with a prescribed H_{∞} disturbance attenuation level. The designed non-fragile H_{∞} controller is constructed via convex optimization by guaranteeing its sufficient condition in terms of feasible linear matrix inequalities (LMIs). Simulation results are given to show the effectiveness of the proposed control approach.

The objective of this chapter is to study the problem of vibration control analysis and synthesis in a vehicle engine-body vibration structure. It is assumed that the actuator is subject to a time-varying delay for control of bounce and pitch vibrations. Based on a Lyapunov-Krasovskii functional and using some free weighting matrices, delay-dependent sufficient conditions for designing desired state- and output-feedback controllers are given in terms of linear matrix inequalities (LMIs). The state- and output-feedback controllers, which guarantee asymptotic stability with a prescribed γ-level L_{2}-gain (or H_{∞} performance), are then developed directly instead of coupling the second-order model to a first-order system. The controller gains are determined by convex optimization over LMIs. Simulation results are included to demonstrate the validity and applicability of the technique.

This chapter focuses on H_{∞}, fuzzy control of suspension systems under actuator saturation. The Takagi-Sugeno (T-S) approach is used to model the suspension system (quarter, half and full cars) by interpolation of different local linear models. A nonlinear state feedback control parallel distributed compensation (PDC) is employed for designing control system. The main idea of this controller consists in designing a linear feedback control for each local linear model. To address the input saturation problem, both constrained and saturated control input cases are proposed. In the two cases, H_{∞}, stabilization conditions are derived using Lyapunov method. Moreover, a controller design with the largest domain of attraction is formulated and solved as a linear matrix inequality optimization problem. An application to quarter-car suspension system is given. Our simulation results show that both saturated and constrained controls can stabilize the resulting closed-loop suspension quarter car via PDC control and eliminate the effect of external disturbances despite the presence of saturation. Indeed, the main roles of car suspension systems which consist of improving ride comfort of passengers and the road holding capacity of the vehicle are achieved.

This study presents a novel reduced-order non-linear observer for vehicle velocities estimation based on vehicle dynamics and Unified Exponential tire model. Yaw rate is chosen to construct the reduced-order observer since it can be conceived as the function of vehicle velocities. The observer is designed such that the error dynamics system is input-to-state stability (ISS), where model errors including mass and CoG variation, and estimation or measurement error of the maximum tire–road friction coefficient are considered as additive disturbance inputs. Then, the condition of the observer gain satisfied is obtained by the ISS analysis and the lower observer gain is obtained through the convex optimisation described by the linear matrix inequalities. The proposed observer requires fewer tuning parameters and thus indicates an easier implementation compared with the existing extended Kalman filter. Simulation results demonstrate the effectiveness of the proposed reduced-order non-linear observer, which is also validated through experimental data from Hongqi vehicle HQ430. Furthermore, its computational efficiency is shown based on the laboratory Field Programmable Gate Array and System on a Programmable Chip testing platform.

An approach for eigenvalue assignment in linear descriptor systems via output feedback is proposed. Sufficient conditions in order that a given set of eigenvalues is assignable are established. Parametric form of the desired output feedback gain matrix is also given. The approach assigns the full number of generalised eigenvalues, guarantees the closed-loop regularity and overcomes the defects of some previous works.

A controllability condition of a siphon composed of three elementary ones in a class of Petri nets, namely S3PR, is developed. Under the condition, a maximally permissive liveness-enforcing supervisor expressed by a set of monitors (control places) can be decided by an algorithm with polynomial complexity for an S3PR if every dependent siphon is m-composed with m ≤ 3.

This study presents new sufficient conditions for Hurwitz and Schur stability of interval matrices. Tight bounds for the spectrum of interval matrices are estimated using computationally simple optimisation problems. The conservativeness is reduced further by application of ordinary similarity transformation. A necessary and sufficient vertex based criterion for the stability of a subclass of interval systems in continuous and discrete-time cases is also proposed. This enables the spectra for this class of interval systems to be determined exactly. A selection of various examples adopted from existing literature is used to demonstrate the utility of the proposed criteria.

Presented is a square root algorithm in _{q} which generalises Atkins's square root algorithm [see reference 6] for *q* ≡ 5 (mod 8) and Müller's algorithm [see reference 7] for *q* ≡ 9 (mod 16). The presented algorithm precomputes a primitive 2^{s}-th root of unity ξ where ** s** is the largest positive integer satisfying 2

_{s}|

*q*− 1, and is applicable for the cases when

*s*is small. The proposed algorithm requires one exponentiation for square root computation and is favourably compared with the algorithms of Atkin, Müuller and Kong

*et al.*

This study investigates control and decision strategy for the failure prone manufacturing process, which is modelled as a two-mode Markovian jump system (MJS). Considering the historical effects on the system, the mode transition rate matrix (MTRM) is time-varying instead of homogeneous. A piecewise homogeneous MJS is thus proposed to characterise this phenomenon, in which the MTRM is homogeneous during certain time intervals but non-homogeneous for the whole time interval. By regarding each homogeneous MTRM as one event, all the MTRMs over the whole time interval will take values in an event set and be governed by a higher-level Markov chain. To ensure such system operates normally with high probability, the decisions including preventive maintenance and corrective maintenance are introduced to adjust the higher-level Markov chain. Motivated by this, a new joint performance, consisting of both cost function for decision making and controller design, is developed. Optimal decisions are obtained by an iterative algorithm whose convergence is proved, as well as an optimal controller is designed. The effectiveness of this method is demonstrated by simulations.

The present study proposes a new scheme for detection and isolation of incipient sensor faults for a class of uncertain non-linear systems by combining sliding mode observers (SMOs) with a Luenberger observer. Initially, a state and output transformation is introduced to transform the original system into two subsystems such that the first subsystem (subsystem-1) has system uncertainties but is free from sensor faults and the second subsystem (subsystem-2) has sensor faults but without any uncertainties. The sensor faults in subsystem-2 are then transformed to actuator faults using integral observer-based approach. The states of subsystem-1 are estimated using an SMO to eliminate the effects of uncertainties. However, since subsystem-2 does not have any uncertainties, the incipient faults present in this subsystem are detected by designing a Luenberger observer. These faults are then isolated by applying a bank of SMOs to subsystem-2. The sufficient condition of stability of the proposed scheme has been derived and expressed as linear matrix inequalities (LMIs). The design parameters of the observers are determined by using LMI techniques. The effectiveness of the proposed scheme in detecting and isolating sensor faults is illustrated considering an example of a single-link robotic arm with revolute elastic joint. The results of the simulation demonstrate that the proposed scheme can successfully detect and isolate sensor faults even in the presence of system uncertainties.

The concept of networked override control system (NOCS for short) is proposed and its configurations are investigated in detail. Override control system, wherein the control loops are closed via real time networks, is called networked override control system. Based on the proposed node-device connectivity matrix and network transmission matrix, three typical configurations of NOCSs are explicitly proposed and characterized. The configuration diagrams and block diagrams of them are also presented. Future research directions are also pointed out.

This paper briefly describes the framework of Lie group classifier, then Lie group classifier is introduced to detect fault of bearings, aiming at the characteristics of bearing fault vibration signals. Firstly, training feature set and test feature set are constructed from fault vibration signal. The two sets consist of mean value, energy, root-mean-square value, peak value, crest factor, kurtosis, shape factor, clearance factor. Secondly, training feature set is applied to Lie group classifier to compute classifier parameters. Thirdly, bearing fault is diagnosed by Lie group classifier based on test feature set. The results show that this method can detect fault with high accuracy rate and it presents a new method for bearing fault diagnosis.

In the textile industry, the classfication of woven fabric is usually manual. To improve work efficiency, this paper purposes a novel approach to extract image features for woven fabric's recognition automatically. Firstly, the local binary pattern method and the gray level co-occurrence matrix are adopted to compute the fabric image features. Then, the principal component analysis is utilized to reduce the high dimensional feature data. Lastly, a support vector machine is used as a classifier to recognize the woven fabric type. The experiments show that these methods can automatically and accurately classify the plain weave fabrics, twill weave fabrics and satin weave fabrics.

This paper is concerned with the inverse eigenvalue problems for symmetric Toeplitz matrices. A kind of inverse problem for constructing a real symmetric Toeplitz matrix from the given k eigenpairs is proposed. By using the special structure of symmetric Toeplitz matrices, the Kronecker product and the vec operator of matrices, the problem is transformed into the system of linear equations. Some necessary and sufficient conditions for the solvability of the problem are given. The general solutions of the problem are presented.

This study presents a mathematical method to calculate the generating function of the specialized mechanisms in type synthesis with design constraints. First, the link permutation group is derived from a candidate kinematic chain according to the combinatorial theory. Next, according to the types of design constraints, joint, path, and adjacent (or non-adjacent) pair groups are derived from the link group respectively. Then, the generating function of these groups can be calculated mathematically based on four well defined operators and basic groups. The generating function is a polynomial to express the results of specialized mechanisms subjected to a specific design constraint. The benefit of the method is that the results of the type synthesis can be calculated directly by mathematical manner without any inspection of isomorphism.

The problem of norm invariance property of two-spin half systems is discussed in this paper. Based on the basis of tensor space, the Liouville-von Neumann equation of two-spin half systems is transformed into the coordinate differential equation by using matrices of adjoint operators of two-spin half systems. Then, norm invariance property of trajectory of the transformed coordinate differential system is established.

The authors consider the kinematic concepts of a new lower-limb rehabilitation device in closed muscular chain. The proposed control structure is based on a trajectory generator and a continuous non-linear tracking controller. The human efforts applied to this device are considered as external disturbances to the system's dynamics and as inputs to the trajectory generator and allow safe voluntary control of the system by the user. A *H*_{∞} control structure based on a Takagi–Sugeno descriptor model is proposed to track the desired trajectories and to attenuate external disturbances. Stability conditions are given in terms of linear matrix inequalities using a fuzzy Lyapunov function. Finally, the simulation results of the proposed control structure for the new rehabilitation device during isokinetic movements illustrate the efficiency of the proposed approach.

The study paper deals with sensor fault detection problem for a class of linear uncertain systems with bounded disturbances and non-zero constant reference inputs. The sensor faults are modelled as multi-mode, named as fault-free mode and faulty modes. A steady-state-based approach is proposed to detect the sensor faults. The steady-state-based approach can be used to detect lock-in-place sensor faults with arbitrary small magnitudes, which has not been well investigated in the literature. A convergent iterative algorithm based on linear matrix inequalities is given to obtain the solutions. A numerical example is given to illustrate the effectiveness of the proposed methods.

A product generation model (PGM) integrates information from several different generations of a product to facilitate remanufacturing and eventual reuse, by storing all the information from each product generation. Using this method, a new or remanufactured component is checked for compatibility with the existing system before it is installed. New PGM architecture based on polychromatic sets uses sets and Boolean matrices to manage the logical relationships between the different generations of product data and is a highly efficient data management system to control multiple lifecycles of a product. The implementation process of this system for remanufacturing and reuse based on the product generation model is analyzed in this paper.

An linear parameter varying guidance method for the hypersonic phase of a space re-entry vehicle is presented. The suggested guidance scheme, relying on flatness approach, is applied to the non-linear model of the European Atmospheric Re-entry Demonstrator. It is shown that the overall guidance scheme achieves robust stability and performance, even in the presence of entry point kinematics dispersions. The design problem is formulated and solved using a finite set of linear matrix inequalities. Finally, Monte Carlo simulation results are presented to demonstrate the effectiveness of the suggested approach.

A backstepping-based tracking control design for uncertain mobile robot systems with non-holonomic constraints is presented. For avoiding the singularity and the necessity of the repeated differentiation of the virtual controller, high-degree polynomials of the affine functions are generally included in many existing kinematic controllers. That unfortunately would cause the possible blowup of the actuators for high-order kinematic systems (e.g. a trailer-type mobile robot) in high-speed motions. Regarding this, an exponentially modulated linear stabilising function is included in this design to alleviate such a difficulty. Next at the dynamic design level, an adaptive control algorithm is developed for attaining the global asymptotic tracking stability of the overall closed-loop system. Two case studies of a unicycle-like and a trailer-type wheeled mobile robots are conducted in the final to demonstrate the effectiveness of the proposed design.

The lifting methodology can be used for simplifying the closed-loop stability study of a system in which the measurement data are acquired at different frequencies. This is because the lifting operators allow treating this kind of systems as if there is only one control frequency, which reduces the complexity of the problem in a very important way. The four-rotor microhelicopter designed by the authors, whose control is faced, is a nonlinear plant with sensors operating at two different frequencies. First, the system is linearised cancelling the rotors dynamics. Then, the authors implement a model reference adaptive control structure for identifying the gains of the linear reference plant and performing the adaptive control of the microhelicopter. At this point, the system stability study is carried out by just computing the eigenvalues of the closed-loop states matrix thanks to the lifting operators.

In this paper, the indexes system of green degree of biodegradable packaging materials is built and the fuzzy analytical hierarchy process (FAHP) methodology based on life cycle assessment (LCA) is employed to analyze and assess this system. The qualitative assessment is gained by the survey and the statistics theory is employed to deal with the qualitative data. The judgment matrix is built and the maximum characteristic root and vector are computed by the sum and product method. Then the relative importance degree of every influence factor is computed and the comprehensive importance degree of every influence factor is gained. The membership function of every influence factor is established by logical reasoning assignment method, then the membership degree is gained. According to the comprehensive importance degree and the membership degree of every influence factors, the green degree of biodegradable packaging materials is generally assessed. The green degree of biodegradable packaging materials is compared with that of plastic material, and the result is that the biodegradable packing materials have higher green degree then that of plastic material. (5 pages)

This part reviews complex-variable algebra.

Computation of elementary siphons proposed by Li *et al.* is essential for deadlock control and expensive since complete siphon enumeration of the Petri net is needed, and the number of strict minimal siphons (SMS) grows quickly and exponentially with the size of the net. They assumed that the siphon constructed from each resource circuit is an elementary one and proposed a polynomial algorithm to compute elementary siphons. However, the author demonstrates a counter example where there may be an exponential number of resource circuits. Hence, constructing elementary siphons from resource circuits will result in an exponential number of elementary siphons, which is wrong. The author then develops a polynomial algorithm to find elementary siphons, which also constructs all SMS on the way. This is because, in the method proposed by Li *et al.*, a linear algebraic expression must be established for each dependent siphon, which implies, all SMS must be located. However, all elementary siphons with polynomial complexity can be located.

Motivated from some practical industrial processes, an optimal fault tolerant control (FTC) scheme is studied for stochastic continuous dynamic systems with time delays using output probability density functions (PDFs). Different from the classical FTC problems, the measured information is the PDFs of system output rather than its value, where the B-spline expansion technique is applied so that the output PDFs can be formulated in terms of the dynamic weightings. For the established weighting system with nonlinearities, uncertainties and time delays, the concerned FTC problem is investigated by using robust optimisation techniques. A linear matrix inequality (LMI) based feasible FTC method is presented to ensure that the fault can be well estimated and compensated, where the generalised *H*_{∞} performance is optimised for the time-delayed systems with the non-zero initial condition and the truncated norms. Simulations for a model in the paper-making process are given to demonstrate the efficiency of the proposed approach.

A formulation of stability for formation flying spacecraft is presented. First, a formation is defined via control interactions between the spacecraft. Then, stability is formulated on the basis of input-to-output stability with respect to a partitioning of the formation dynamics. The particular form of input-to-output stability used here is based on the peak-to-peak gain of a system from its input to its output. This formulation of stability is shown to be useful in characterising disturbance propagation in the formation as a function of the partition interconnection topology, and also in analysing the robustness of sensing, communication and control topologies. Stability analysis results are presented for hierarchical, cyclic and disturbance attenuating formations in terms of the input-to-output gains of the partitions in the formation. Finally, Lyapunov stability analysis results are provided in terms of linear matrix inequalities for a general class of formations.

The plastic electromagnetism dynamic extruder has gained wide applications because of its novel structure and fine engineering performance. In the polymer processing, melt temperature and melt pressure control is crucial to the quality of the extruded product. A new fuzzy decoupling control algorithm of melt temperature and melt pressure for the novel extruder is introduced in the transfer function matrix system, which is obtained through the experimental data with system identification. The control system is implemented on programmable computer controller. Experimental results show melt temperature and melt pressure can be successful individually controlled by the heater power and the screw speed. The good system performance verifies the control strategy's validity.

The present investigates the architecture singularity of a class of parallel manipulators. In general, singularity of parallel manipulators can be categorized into inverse and forward kinematic singularities. Based on the kinematics, the inverse Jacobian matrix of the parallel manipulator is factorized into three parts as: limb length diagonal matrix, structure parameter matrix and the motion parameter matrix so that the singularity analysis becomes convenient. Because each limb length is not zero, there does not exist inverse singularity. Only forward kinematic singularity exists in the parallel manipulators. The forward kinematic singularity is divided into architecture singularity and motion singularity. Architecture singularity is global and results in no solutions for forward kinematics. It should be avoided at the design stage. The class of parallel manipulators becomes architecture singularity as long as their six vertices of the platform are placed in a quadratic curve. Since the architecture singularity can be algebraically expressed, the constraints to avoid the undesired effects of the architecture singularity can be straightforwardly implemented for the design of the parallel manipulators and the planning of workspace and trajectory.

In process planning, how to use manufacturing features to obtain an optimal process planning is the essential of computer-aided process planning (CAPP) system. The main goal of CAPP system is to translate the manufacturing features into machining operations and sequence the machining operations of the part in a feasible (by some technological constraints) and effective (by some economical standards) order. In this paper, we construct a process-planning model (PP model), which consists of three parts: the features framework, the precedent relation net and the sequencing mathematical model. The features framework makes a mapping from manufacturing features into machining operations. A semantic net named the precedence-relations-net reflects the precedence relationships among the machining operations. And we employ the vectors and the matrixes to construct a mathematical sequencing model. Firstly, a part is decomposed into several basic geometrical units, namely, U1,U2,...UN. For each unit - Ui, two vectors, named Fi and Pi represents the features and machining operations of Ui. Finally, a matrix named PP is used to memorize the process plan, and a matrix; namely, PO (performing objects) represents the object of machining operations.

In the application of active reflector units supporting mechanism for a large spherical radio telescope (five-hundred meter aperture spherical radio telescope: FAST), a spatial three-degree-of-freedom (DOF) parallel mechanism combining two degrees rotation and one degree translation is investigated. In this paper, the mechanism is described in detail and its inverse kinematics solutions are derived. The parasitic motion of this mechanism is analyzed, and the relationships between the parasitic motions and independent motions of the mechanism are illustrated, followed by the Jacobian matrix of the velocity equation. The distribution of conditioning index on the workspace of the mechanism is obtained. And the workspace of the mechanism is numerically generated. The analysis results prove that the parasitic motion is neglectable compared to the independent motion in this application and the mechanism can be used as the supporting mechanism of spherical radio telescope.

Dual response surface methodology (DRSM) and nonparametric methodology (NPM) are main approaches used to achieve robust parameter design (RPD) of industrial processes and products. When the relationship between influential input factors and output quality characteristic of a process is very complex, both approaches have their limitations. For DRSM, it fails to fit the real response surfaces of process mean and variance by using the second order polynomial models. For NPM, it is hard to optimize parameters of fitting equation, and it needs more experiments as well. From a machine learning perspective, this paper generalizes RPD as a restricted active learning problem and proposes a new approach to achieve it. It fits process mean and variance responses by support vector machines (SVM), and then optimizes levels of design parameters by genetic algorithm. In order to reduce experiment times, the influence of priori knowledge on generalized error of fitting model is studied. Then a prior knowledge based experiment design is developed. Moreover, the approach selects the form of kernel function and optimizes parameters in SVM by comparing the upper bounds of generalized error of different SVM models without extra samples. The example given in the paper shows that, the generalized error and the experiment times of the approach decrease by no less than 45% and 39% respectively, compared with traditional approaches. All these results demonstrate the adaptability and superiority of the approach proposed in the paper.

It is difficult to get solutions that can meet the requirements of high positioning accuracy and real time control simultaneously among the infinite solutions of a redundant robot. Based on weighted least-norm method (WLNM), an optimized algorithm for inverse kinematics solution of redundant modular robots, with which the joint limits can be avoided, is presented in this paper. According to the characteristic of robot global wrist organ, the position and pose of the robot tag end can be resolved separately, therefore the computing time is reduced without decreasing the solution accuracy. Recently, an Intravehicular Robot Service System's Ground Demonstration for Space Station has been built in the Space Robot Lab of Bupt, and the operation object of the demonstration is a 9-DOF modular reconfigurable robot. Through the experiments of pulling drawers and pressing buttons by the 9-DOF robot, the accurate and real-time solutions are given to show the applicability and effectiveness of the proposed algorithm. The experiment results demonstrate that the positioning accuracy is up to ±2.0 mm and single-step computing time is less than 1 ms.

The input-output energy decoupling is put forth for the complex electromechanical tension system problem including strong coupling, multi-variance, uncertainties, etc. The aim is that an energy of any input controls mainly the energy of a corresponding output and influences the energy of the other as weakly as possible. After the looper height and tension control system has been modeled, a H_{∞} robust control algorithm based on input-output energy decoupling is proposed in terms of the solution of linear matrix inequalities (LMI). Finally, the input-output energy decoupling algorithm is applied to the tension system, and the simulation results show that the method has satisfactory decoupling performance. The validity of the designed controller is validated.

A controller based on first-order decoupled equations of motion for application to rigid serial manipulators is presented. The equations result from a modification of equations expressed in generalised velocity components form. It is shown that using the proposed quasi-velocities i.e. normalised generalised velocity components (NGVCs) leads to differential equations that contain the identity mass matrix (instead of a diagonal matrix). Using the proposed controller and equations written in terms of NGVCs it is possible to obtain information on the system dynamics. The considered controller is stable in the Lyapunov sense. Experimental results obtained on a two-degree-of-freedom manipulator illustrate the effectiveness of the proposed technique.

Transient conditions such as switching operations and faults cause the generation of travelling waves on power transmission lines. Spatial current and voltage distributions on the transmission line are computed in the time domain using the state-space technique. The state-space representations of the transmission lines for short- and open-circuit faults and for various types of terminations are given. The results obtained by the method are compared with the solutions obtained in the frequency domain.

The authors analyse the steady-state behaviour of a class of cross-directional controllers that are pertinent to general web-forming processes. Their analysis is framed in terms of the controllable space prescribed by the interaction matrix and general discrete orthonormal basis descriptions of both the input and output space under the assumption of closed-loop stability. The specific choice of controller defines (whether explicitly or implicitly) an additional assumed controlled space. It is well known that the controllable space determines a lower bound on output variation. They examine the implications of integral action and provide sufficient conditions for the steady-state output variation to achieve this lower bound. They confirm some intuitive results that connect the optimal constrained and unconstrained steady-state solutions for model-based control with no model mismatch. Model mismatch is usually detrimental to steady-state performance. This effect is interpreted in terms of leakage between the controllable and assumed controlled spaces, as well as their respective orthogonal complements.

A

It is of practical interest to identify which processes will benefit significantly from the use of constrained control algorithms such as model predictive control, and which will not. Explicit conditions are derived that identify whether a particular process may benefit from constraint handling. These conditions are also useful for understanding the interactions between design and control for a particular system, especially for actuator placement and selection. The conditions are computable for a large-scale system directly from its transfer function model, a simulation model (e.g. defined by a set of ordinary/partial-differential equations and algebraic conditions), or experimental input–output data. The formulation considers the effects of measurement noise, process disturbances, model uncertainties, plant directionality and the quantity of experimental data. The conditions are illustrated by application to a paper-machine model constructed from industrial data.

Although the full radix-4 CORDIC algorithm is efficient compared to the standard radix-2 version, the scale-factor overhead causes its improvement to be limited. In this work, an algorithm and its associated architecture have been proposed for parallel compensation of the scale factor for the radix-4 CORDIC algorithm in the rotation mode. The proposed method, which makes no prior assumptions about the elementary angles of rotation, reduces the latency from *n* to (*n*/2)+3, where *n* is the precision length in bits, at the cost of a reasonable increase in hardware complexity. The architecture presented relates to the redundant signed-digit number system. The architecture has been modelled in VHDL and simulated to establish its functional validity.

The speed of simulation of power system dynamics has been one of the topics most concerned with on-line security assessment. This paper proposes a new method for forming the constant Jacobian matrix for enhancing the speed of system simulation. By using the constant Jacobian matrix approach in system simulations, both for post-fault and fault-on duration, simulation efficiency is greatly enhanced. Techniques for speeding up the constant Jacobian matrix approach are discussed. Theoretical analysis is presented to demonstrate how the constant Jacobian matrix approach can be extended to a power system with generator controls. Simulation results with the constant Jacobian matrix approach in the 10-generator New England test system and the North China power system are compared with the results obtained by the use of commercial software BPA.

Various ray-tracing methods have been developed for wireless propagation predication. Most of them are hybrid 2D and 3D models (see Athanasiadou, G.E. and Nix, A.R., IEEE Trans. Veh. Technol., vol.49, no.4, p.1152-68, 2000; Liang, G. and Bertoni, H.L., IEEE Trans. Antennas Propagat., vol.46, no.6, p.853-63, 1998). They assume the walls are vertical, roofs and ceilings are horizontal and the ground is flat. These assumptions are not always true. This paper presents a new 3D ray-tracing method based on 3D geometry and vector calculations. Propagation path concepts of triangular reflection pyramid ray-tubes and diffraction hollow cones have been developed. This method applies to different terrains and both indoor and outdoor environments. Virtual reality (VR) is used to visualise the environments and line-of-sight (LOS) and non-LOS signal paths and allows us to verify the methods we used.

Obtaining the steady-state operation of a power electronic device by means of brute force computer simulation is not feasible in many practical cases. Fast steady-state algorithms that formulate the steady-state problem as a boundary problem and solve it using Newton's method have been proposed to overcome this difficulty. These algorithms are known as shooting algorithms. An extension of the shooting algorithm for piecewise linear circuits is provided. The complete Jacobian matrix that takes into account the switching instants variation is analytically derived for a state variable formulation of the steady-state problem of a piecewise linear circuit. A computer program PWiseSS based on this algorithm is used to solve a previously proposed test circuit of difficult convergence as well as to solve a realistic six-pulse converter of interest to the power electronics engineer.

A direct method for frequency stability assessment of power systems is proposed in this paper, which is based on the latest Jacobian matrix of the Newton-Raphson load flow calculation. The method can directly calculate the final system frequency after the last switching without step-by-step integral, and the system frequency stability can be determined. The proposed method has been applied to the New England 68-bus system, and the results show that the method is of good accuracy and the fine prospect of online application.

In many applications neural networks use temporal information, i.e. any kind of information related to a time series. Temporal information can be either represented within a network using a dynamic network paradigm or embodied in the input features of a network. The paper presents two methods for an explicit use of temporal information in input features. A least-squares approximation of signals with orthogonal polynomials is used to infer information about trends in a signal (average, increase, curvature, etc.). Input information about the length of a time series up to a certain point in time may act as a decreasing threshold making the network more and more sensible to changes in other input features. The advantages of the two methods are demonstrated by means of a real-world application example, tool wear monitoring in turning.

Often in process control, it is necessary to use extra measurements, or so-called secondary outputs for monitoring processes. Traditionally, the selection of these outputs is based on criteria which need to be calculated scheme-by-scheme resulting in a combinatorial problem. In this work, it is shown that these secondary outputs can be selected using an efficient measure, the output effectiveness (OE) when the outputs are scaled in a special way. This method does not need any scheme-by-scheme calculation so that the combinatorial problem is avoided. Since the OE measure is dependent on output scaling, its sensitivity to this scaling is also discussed. A scaling sensitivity matrix is derived for the designer to quickly determine the effect of different choices of scaling factors on the OE measure. This information can then be used for efficient output selection. This is demonstrated on a distillation example.

In linear control theory the frequency domain approach and the state-space approach are equivalent. But for the implementation of numerical algorithms the use of state-space equations is preferred. To avoid the numerical problems caused by a polynomial arithmetic, the use of an interval arithmetic with variable length of the mantissa is suggested. Some basic algorithms for polynomial and transfer-function matrices implemented in interval arithmetic are stated. A control example shows the feasibility of this method.

In this paper, a new fault isolation method is proposed. This method is based on the inverse sensitivity analysis. The idea is to identify input command and parameter perturbations using the information provided by the output trajectory deviation and the sensitivity matrices. The estimated perturbation is then used for fault isolation and possibly system reconfiguration. The proposed fault isolation method has been applied to a simulated aircraft control system and the results confirm the effectiveness of this sensitivity analysis approach.

Local model (LM) networks are applied to the identification of the global nonlinear dynamics of a turbogenerator excitation loop. A hybrid algorithm is used to optimise the learning process. Extensive use of plant `a priori' information is used to form an initial estimate for the nonlinear interpolation regions. The resulting model was found to describe the behaviour of the nonlinear generator-exciter system over its entire operating range.

Calculation of controllability and observability Gramians, and the determination of balanced realizations are considered in a symbolic framework. Two different approaches to balancing transformations are explained step by step, and more efficient, simple and numerically stable algorithms based on these two approaches have been implemented. An example taken from the literature is presented in order to illustrate the superiority of the symbolic implementations.

Discusses the issues of robust machining process controller synthesis. In practical cases, operating conditions have strong effects on the process dynamics, and it is very difficult to use a fixed controller to achieve a satisfactory performance. Here, a fuzzy logic inference mechanism is introduced to adjust the controller according to the online measurements of operating variables which define the operating conditions or operating points of the processes, and a linear matrix inequality (LMI) based hybrid approach is developed to achieve robust properties against modelling errors, uncertainties, disturbances, and inaccuracy of online measurements. The simulation results of a design example (an end milling process control) shows that robust stability and satisfactory performance have been achieved.

Modern symbolic computational systems which perform automated manipulation of mathematical variables offer insights during modelling and problem solving which remain otherwise partially or wholly obscured to the analyst. The classic inverted pendulum model is re-visited, and previous work concerning the systems controllability is investigated. In particular, the ability of the software to factorise complicated multivariable polynomials is exploited to identify, in fully general form, the anticipated pole-zero term cancelling throughout the transfer functions of the system when it is in a state of un-controllability. All three balancing problems associated with the two link pendulum are treated, and the phenomenon of non-controllability is examined in this way along the entire `curve of non-controllability' which, within the approximation of linearity, theoretically exists for each when damping is present.

The problem of quality control of radiological systems is discussed in relation to the management and quantitative tools normally applied to it. An alternative approach is to consider the problem in terms of a control loop in which the sets of quality control measurements are compared with their previous values in the context of a numerical model of the system to produce quantitative corrections. A preliminary study of the method applied to mammographic quality control is discussed. By modelling the system with an appropriate set of simultaneous linear equations relating changes in the controlled parameters to the quality control measurements obtained, it is possible to identify quantitative changes in the controlled parameters from measured quality control data using the inverse of the model in matrix form. This method essentially encapsulates knowledge about the system in the form of the linear model. This is distinct from current work attempting to apply artificial intelligence knowledge-based techniques to the problem. (4 pages)

Sparse-matrix solution is a dominant part of execution time in simulating VLSI circuits by a detailed simulation program such as SPICE. The paper develops a parallel-block partitionable sparse-matrix-solution algorithm which exploits sparsity at the matrix block level as well as within a nonzero block. An efficient mapping scheme to assign different matrix blocks to processors is developed which maximises concurrency and minimises communication between processors. Associated reordering and efficient sparse storage schemes are also developed. Implementation of this parallel algorithm is carried out on a transputer processor array which plugs into a PC bus. The sparse matrix solver is tested on matrices generated from a transistor-level expansion of ISCAS-85 benchmark logic circuits. Good acceleration is obtained for all benchmark matrices up to the number of transputers available.

The capabilities of computer algebra extend well beyond the bounds of mathematics. The author describes some of the less obvious ways in which these powerful software packages can come to the help of the busy engineer in many fields, including text processing, graphics etc.

A method of controlling certain types of nonlinear dynamical systems whose dynamics can be modelled by a multilayer neural network is proposed. The control algorithm assumes that the plant equations are not known but the dimension of the system is known. The control input is derived by inversion of a forward neural network via the Newton Raphson method. During inversion of the multilayer neural network some optimal control senses are resolved. To suppress the control error due to the modelling error of the forward neural network, the inversion controller with a conventional feedback controller is proposed, which provides a better performance than a pure inversion controller. The proposed algorithm shows various advantages, and computer experiments on a bioreactor prove the effectiveness of this algorithm.

A new design method of discrete-time model reference adaptive control for nonminimum phase systems is presented, with disturbances using approximate inverse systems obtained from the long division method. It is assumed that the disturbances are described by a polynomial function of time with known degree and unknown coefficients. The proposed scheme uses only input and output data, and the existence of bounds for all signals is proved. This scheme also assures that plant output converges to the reference model output. The results of computer simulation are also presented to illustrate the effectiveness of the proposed method.

The A-function method is extended to analyse a relay feedback control system with additional nonlinearities in the feedback loops. The situation considered is where the output of the plant and/or its successive derivatives are fed back to the input through nonlinearities that are assumed to be of polynomial type. An example is also given to show that, in some cases, the method can be used in systems with saturation or a linear segmented nonlinearity in the feedback path.

This paper outlines the method of obtaining the frequency response functions of a rotor system with strong gyroscopic effect and simulating it using MATLAB. The rotating effect causes unsymmetry in the system matrices, resulting in complexity in decoupling the mathematical models of the system for the purpose of modal analysis. A different method is therefore required, which can handle general system matrices rather than symmetrical matrices, which is normal for passive structures. In this paper the mathematical model of an overhung rotor system with two degrees of freedom is expressed. This model is then used to extract the right and left eigenvalues/vectors and subsequently the frequency response functions are extracted and simulated. MATLAB is used to carry out such simulation, since it has good capability for eigen analysis and also good graphical facility. The reflection of splitting of critical speeds of a rotating rotor on the frequency response functions are shown.

This paper presents a new parallel-in-space algorithm for power system transient stability simulations. The nonlinear differential equations are discretized by applying the trapezoidal rule and solved together with the nonlinear algebraic equations for each time step. A network partitioning scheme, which is based on the subdivision of the factorization path tree of the network matrix, is proposed to exploit the parallelism-in-space of the transient stability problem. The parallel version of the very dishonest Newton (VDHN) method, in which the parallel algorithm for solving large sparse network matrix equations is incorporated, is developed and tested on a distributed memory message passing multicomputer. Test results on a sample power system are presented to show the performance of the proposed algorithm.

Local model networks represent a nonlinear dynamical system by a set of locally valid submodels across the operating range. Training such feedforward structures involves the combined estimation of the submodel parameters and those of the interpolation functions. The paper describes a new hybrid learning approach for local model networks that uses a combination of singular value decomposition and second order gradient optimization. A new nonlinear internal model control scheme is proposed which has the important property that the controller can be derived analytically. Simulation studies of a pH neutralization process confirm the excellent modelling and control performance using the local model approach. (3 pages)

The backstepping control design algorithms described by Krstic et al. (1995) provide a systematic framework for the design of regulating strategies suitable for large classes of nonlinear uncertain systems. However, the equations arising at the successive steps are usually too complicated to be computed by hand. We consider here a symbolic toolbox which implements a general algorithm for the design of dynamic adaptive controllers following the basic ideas of backstepping with tuning functions without transformation into canonical forms. This algorithm is applicable to observable minimum phase systems not necessarily in triangular form and also to uncertain nonlinear systems in triangular forms. Additionally the control can be generated by a sliding mode approach. (3 pages)

Geometrical symmetry often occurs in computational electromagnetics. However, it is generally not taken into account when the excitations do not share this symmetry. A rationale is required, and group theory gives the only valuable tool for this purpose. It provides a symmetric decomposition of any problem that allows its study on a reduced part of the initial geometry. This way of treating field problems generally leads to substantial computational savings. The symmetry concept is applied in the paper to 3-D linear eddy-current analysis, where the numerical scheme used is a mixed FEM–BEM method. Detailed examples are presented to demonstrate the efficiency of the use of symmetry.

This paper presents the method used to derive the oscillation condition by using symbolic calculus. The program is based on the full nonlinear Barkhausen criterion method. The behaviour of an oscillator is described by a complex polynomial called the characteristic polynomial. This polynomial enables us to calculate the steady state features of the oscillation as well as the differential equation for transient analysis in the time domain. The literal determination of this characteristic polynomial involves lengthy algebraic calculations and cannot be done by hand as the electronic oscillator circuit involves too many components. We recently developed a formal calculus program allowing to automatically obtain all necessary equations for oscillation analysis. We propose new methods to calculate them in an optimal form.

A conventional diagonal controller can be designed from very limited process information. In the SVD control structure, a diagonal controller is applied to orthogonal sums and differences of the inputs and outputs. In this work, the process knowledge needed for the design of an SVD controller is analyzed. In contrast to conventional decentralized controllers, the SVD controller can compensate for the process directionality of ill-conditioned processes. The dual composition control problem of distillation columns is of particular interest, since reliable models for these columns are quite hard to obtain.

The problem of stabilising a MIMO plant via output feedback controllers of a given degree was recently tackled via linearisation around some special degenerate compensators. This can be numerically implementated as an ɛ-perturbation method. The solution is in the form of a perturbation series which can be constructed by repetitively solving a set of linear equations, coming from the expansions (in ɛ and s) of the original pole placement equations. This expansion can be done almost trivially in any symbolic language using standard symbolic commands. The code is only a few lines long and can be done by the nonexpert. There is no need to understand the algebra of the problem, which involves tensor, polynomial algebra and some combinatorics since the load of the expansion is taken solely by the symbolic package. (4 pages)

This paper has dealt with the prototype symbolic manipulation CAD system-Symbolic Control Toolbox-running on MATLAB. The functions are implemented in the conventional numerical CAD system. Compared with numerical CAD our system has the following advantages: there exists no roundoff or truncated error; the adopted algorithms are so systematic and well-defined that functions are implemented easily over various rings corresponding to control theories by using the symbolic computation; and the results of the system can be extended easily to n-dimensional system theories.

A novel algorithm for solving nonlinear discrete time optimal control problems with model-reality differences is presented. The technique uses dynamic integrated system optimisation and parameter estimation (DISOPE) which achieves the correct optimal solution in spite of deficiencies in the mathematical model employed in the optimisation procedure. A new method for approximating some Jacobian trajectories required by the algorithm is introduced. It is shown that the iterative procedure associated with the algorithm naturally suits applications to batch chemical processes.

A robust fault isolation method is proposed in this paper, which uses state-space parity equations to isolate structured faults. Numerically robust calculations are used to find certain matrices. A workable sufficient condition is given for high threshold isolability. The method is applied to a lathe-spindle system which demonstrates the effectiveness of the method.

The control structure selected has a strong effect on the performance of a closed loop system with respect to its disturbance rejection capability. But the methods used for its selection usually result in a combinatorial problem. To overcome this difficulty, an input pre-screening criterion, the input-disturbance alignment (IDA) measure, is proposed. Some important features of the new indicator and its relationship with other well-known controllability measures are presented. The case study included shows that the IDA can be used for efficient selection of manipulated variables from a large number of candidate inputs. These then form the best control structure for disturbance rejection.

This paper reports the use of a general technique to combine several different methods to solve complex systems of algebraic equations in the context of load flow calculations of electrical power networks. Such a combinations of methods, referred to as 'team algorithms', seem specially well suited to be used with distributed memory computer systems, in an asynchronous environment. Experimental results solving example problems in a commercially available parallel computer system show that a 'synergetic effect' with considerable speedup can be obtained using these 'team algorithms'.