In this study, a fault detection and identification (FDI) scheme are proposed for constrained stochastic linear hybrid systems (CSLHSs) based on our proposed constrained innovation hybrid estimator (CIHE). CSLHSs are stochastic linear hybrid systems that have state equality constraints on the dynamics of each mode. The CIHE is derived to estimate the CSLHS in such a way that the expectation of the innovations of the mode-matched filters satisfy the constraints. Therefore the constraint information is available in the residual of the CIHE for FDI of not only system dynamic faults but also constraint violations. Each constrained, mode-matched filter is proved to be unbiased, satisfy the constraint, and have smaller estimation error than corresponding unconstrained filters. It is also proved that the CIHE is unbiased and that three residuals from the CIHE have zero mean with a given covariance for different cases of system faults. By monitoring the statistical properties of these residuals, both constraint and discrete faults are detected and identified. The estimation and FDI characteristics of the CIHE algorithm are illustrated using a water tank system as an example.

In this study, the consensus problem of second-order multi-agent systems (MAS) with position-only information is studied. Allowable sampling period for which second-order consensus can be achieved is obtained with two impulsive consensus algorithms. It is shown that if there is at least one eigenvalue of the Laplcian matrix with a non-zero imaginary part, consensus cannot be achieved for sufficiently small or large impulsive periods for both algorithms. Furthermore, the convergence performance of the MAS is optimised. Convergence speed, asymptotical decay factor and per-step decay factor of the error energy are utilised to investigate the convergence performance, and the relationship among impulsive period, topology structure and convergence performance is derived. Finally, numerical examples are given to validate our theoretical results.

To solve the joint-angle and joint-velocity drift problems in cyclic motion of redundant robot manipulators, an acceleration-level drift-free (ALDF) scheme subject to a linear equality constraint is proposed, of which the effectiveness is analysed and proved via the theory of second-order system. The scheme is then reformulated into a quadratic program (QP). Furthermore, two recurrent neural networks (RNNs) are developed for solving the resultant QP problem. The first RNN solver is based on Zhang et al's neural-dynamic method and called Zhang neural network (ZNN), whereas the other is based on the gradient-descent method and called gradient neural network (GNN). Comparison results based on computer simulations between the ZNN and GNN solvers with a circular-path tracking task demonstrate that the ZNN solver has faster convergence and fewer errors. In addition, the hardware experiments of tracking a straight-line path and a rhombic path based on a six degrees of freedom manipulator validate the physical realisability and efficacy of the proposed ALDF scheme and the two RNN QP-solvers. Moreover, the position, velocity and acceleration error analyses indicate the accuracy of the proposed ALDF scheme and the corresponding RNN QP-solvers.

In this studies, adaptive boundary control for a flexible two-link manipulator with a changeable payload at the free-end. Taking into account the infinite-dimensionality of the flexural dynamics, this study proposes a partial differential equation (PDE) model, so that the problem of possible spillover instability caused by the neglect of flexible modes can be avoided. Based on the PDE model, an adaptive boundary control scheme is designed to regulate joint position and suppress elastic vibration while compensating for parametric uncertainties. The asymptotic stability of the closed-loop system is validated theoretically. The effectiveness of the control scheme is also verified by the numerical simulations.

This study presents an analysis about state estimation and dead-time compensation effect over constrained control systems with bounded disturbances and dead-time. It is shown that input-to-state stability and constraint satisfaction can be guaranteed by using an equivalent dead-time free system with measurable states and modified disturbances. This result may be useful to simplify synthesis and analysis of a given constrained control strategy. A linear output feedback control scheme and a tube-based model predictive control strategy are used as motivating examples.

This study presents a sufficient and necessary stability condition for the stability of interval fractional-order systems. An effective constructive method of the value set on the disturbance function of an interval fractional-order system is investigated to reduce the burden of computations for the redundant vertices and edges. Based on the zero exclusion principle, a test function and terminal conditions are proposed to verify the stability of interval fractional-order systems. Finally, a numerical example is given to illustrate the effectiveness of this proposed stability theorem.

This article studies identification problems of multiple linear regression models, which may be described a class of multi-input multi-output systems (i.e. multivariable systems). Based on the coupling identification concept, a novel coupled-least-squares (C-LS) parameter identification algorithm is introduced for the purpose of avoiding the matrix inversion in the multivariable recursive least-squares (RLS) algorithm for estimating the parameters of the multiple linear regression models. The analysis indicates that the C-LS algorithm does not involve the matrix inversion and requires less computationally efforts than the multivariable RLS algorithm, and that the parameter estimates given by the C-LS algorithm converge to their true values. Simulation results confirm the presented convergence theorems.

A new approach is proposed for obtaining discrete-time models of a non-linear autonomous continuous-time system based on classification of, what is called in this study, a discrete-time integration gain. The models are expressed as a product of this gain and the system function that has the same structure as that of the continuous-time system. Sufficient conditions on this gain to make the model exact, in the sense defined in this study, are presented. A new discrete-time model is proposed for non-linear systems, which is approximate in general, but exact for linear systems. The method is applicable to any system that has a Jacobian matrix. As examples, van der Pol and Lorenz oscillators are examined and simulated to show that the proposed discrete-time models perform better than other discrete-time models that are known to the authors to be on-line computable, and tends to retain such key features as limit cycles and chaos, even for relatively large sampling periods.

A distributed control strategy is developed to control the output of multiple distributed generators (DGs) in a coordinated fashion such that these generators develop into a virtual power plant (VPP) in a distribution network. To this end, cooperative control methodology from network control theory is used to make the VPP converge and operate at an optimal output, which is determined by the DGs’ costs and the necessary service assigned by the distribution network. For each DG, the strategy only requires information from its neighbouring units, making communication networks (CNs) among the DGs simple and robust. A set of sufficient conditions under which the proposed method is valid are provided. It is shown that the proposed strategy has the advantages that the corresponding CNs are local and there is no central station collecting global information from the DGs. These features enable the VPP to have both self-organising and adaptive coordination properties. The proposed method is simulated using the IEEE standard 34-bus distribution network.

This study proposes an adaptive gravitational search algorithm (AGSA) which carries out adaptation of depreciation law of the gravitational constant and of a parameter in the weighted sum of all forces exerted from the other agents to the iteration index. The adaptation is ensured by a simple single input–two output (SITO) fuzzy block in the algorithm's structure. SITO fuzzy block operates in the iteration domain, the iteration index is the input variable and the gravitational constant and the parameter in the weighted sum of all forces are the output variables. AGSA's convergence is guaranteed by a theorem derived from Popov's hyperstability analysis results. AGSA is embedded in an original design and tuning method for Takagi-Sugeno proportional-integral fuzzy controllers (T-S PI-FCs) dedicated to servo systems modelled by second-order models with an integral component and variable parameters. AGSA solves a minimisation-type optimisation problem based on an objective function which depends on the sensitivity function with respect to process gain variations, therefore a reduced process gain sensitivity is offered. AGSA is validated by a case study that optimally tunes a T-S PI-FC for position control of a laboratory servo system.Representative experimental results are presented.

This study addresses consensus problems of multi-agent systems (MASs) using dynamic output feedback control under both fixed and switching topologies. We aim to exploit the information structure for the consensusability of MASs. Necessary and sufficient conditions are presented in terms of detectability and stabilisability of the agents, graph topology, and some matrix inequality constraints. These conditions explicitly reveal how consensusability is affected by the intrinsic dynamics of the agents, the communication topology and available information. In addition, this paper provides several constructive procedures for protocol design to achieve consensus, and establishes the so-called separation principle, which simplifies the design procedure greatly.

The purpose of the fault detection and diagnosis of stochastic distribution control systems is to use the measured input and the system output probability density functions (PDFs) to obtain the fault information of the system. In this paper, the rational square-root B-spline model is used to represent the dynamics between the output PDF and the input. This is then followed by the novel design of a non-linear neural network observer-based fault diagnosis (FD) algorithm so as to diagnose the fault in the dynamic part of such systems. Convergency analysis is performed for the error dynamic system raised from the fault detection and diagnosis phase using the Lyapunov stability theorem. Finally, based on the FD information, a new fault-tolerant control based on proportional integral tracking control scheme is designed to make the post-fault PDF still track the given distribution. A simulated example is given to illustrate the efficiency of the proposed algorithms.

This study presents new robust linear matrix inequality (LMI) conditions for robust ℋ_∞ full-order filter design of discrete-time linear systems affected by time-invariant uncertainty and a time-varying state delay. Thanks to the use of a larger number of slack variables, the proposed robust LMI conditions contain and generalise other results from the literature. LMI relaxations based on homogeneous polynomial matrices of arbitrary degree are used to determine the state-space realisation of the full-order filter, that can also be implemented with delayed state terms whenever the time-delay is available in real time. As another contribution, an iterative LMI-based procedure involving the decision variables is proposed to improve the ℋ_∞ filter performance. Numerical experiments illustrate the better performance of the proposed filter when compared to other approaches available in the literature.

In this study, a new consensus problem is introduced for leader–follower multi-agent systems with non-linearity and a distributed adaptive iterative learning control is presented for the consensus problem. With the dynamic of the leader unknown to any of the agent, the proper protocol guarantees that the follower agents can track the leader. The consensus is analysed based on the Lyapunov stability theory. Finally, simulation examples are given to illustrate the effectiveness of the proposed method in this study.

In this study, controllability of discrete-time bilinear systems is studied. Necessary conditions and sufficient conditions for the systems to be controllable are presented. In particular, the sufficient conditions improve some existing results and the necessary conditions are new and easy to verify. Examples and simulations are provided to demonstrate the results of the paper.

In a past study the authors drew attention to the fact that time-varying discrete-time linear systems may be temporarily uncontrollable and unreconstructable and that this is vital knowledge for both control engineers and system scientists. Describing and detecting the temporal loss of controllability and reconstructability requires considering discrete-time systems with variable dimensions and the j-step, k-step Kalman decomposition. In this study for linear discrete-time systems with variable dimensions measures of temporal and one-step stabilisability and detectability are developed. These measures indicate to what extent the temporal loss of controllability and reconstructability may lead to temporal instability of the closed-loop system when designing a static state or dynamic output feedback controller. The measures are calculated by solving specific linear quadratic cheap control problems by means of standard linear quadratic control algorithms. The importance of our developments for control system design is illustrated by means of two numerical examples.