This study deals with design of an adaptive output feedback tracking controller for a class of non-linear systems with unknown fixed control direction. By using neural networks and deriving adaptive rules based on the steepest descent algorithm, the authors present a stable output feedback control scheme, which is applicable to a wide class of unknown complicated non-linear systems. Therefore an approach based on the dynamic back propagation algorithm is proposed to develop the adaption laws for systems with more general model structure. Using Lyapunov's direct method, uniformly ultimately boundedness of all signals of the closed-loop system is also ensured. Moreover, it is shown that the bounds on the tracking errors depend on the designing parameters. Hence, an arbitrarily small tracking error can be achieved by adjusting the parameters properly. Finally, simulation results performed on a non-affine uncertain non-linear system having internal dynamics are given to demonstrate the effectiveness of the proposed scheme and the theoretical discussions.

In this study, the authors deal with a formation of autonomous mobile agents in the distance-based formation control setup, where the formation is represented by a directed cycle. They use gradient control law to stabilise the mobile agents and provide analysis of the behaviour of the agents under the given control law. Although a particular formation shape cannot be achieved by controlling only the inter-agent distances with more than three agents in the plane, at least they can make the inter-agent distances converge to the desired distances and stabilise the agents so that they converge. They found that there are invariant subsets where the agents may not achieve desired distances. However, they show that those invariant sets are not attractive. Simulation results and experimental results verifying their analysis are provided.

This study investigates the optimal guidance problem for reentry vehicles with focus on novel methods for nominal trajectory generation and tracking. To reduce the dimensionality of reentry trajectory optimisation problem, the inversion-based approach is utilised to partly eliminate the differential equations by reformulating the states and controls with some desired outputs. These outputs are parameterised with a mapped Chebyshev pseudospectral method, which is improved by conformal map and barycentric rational interpolation techniques in order to enhance the numerical accuracy for high-order derivatives of desired outputs. On the basis of the obtained nominal trajectory, a robust closed-loop guidance scheme is proposed using receding horizon control, whereas the associated two-point boundary value problem in each guidance cycle is readily solved by differential transformation method. Numerical simulations show that the proposed guidance scheme is feasible and effective for atmospheric reentry.

A limited frequency interval Gramians-based model reduction technique for generalised non-singular discrete time systems is presented. The technique generalises the results of existing limited frequency interval Gramians-based model reduction (of discrete time systems) schemes to general non-singular discrete time systems. Numerical examples are also presented to illustrate the proposed technique.

This study deals with the problem of exponential stability analysis for a class of singular systems with interval time-varying discrete and distributed delays. By constructing a set of improved Lyapunov–Krasovskii functionals, new delay-dependent conditions are established in terms of linear matrix inequalities ensuring the regularity, impulse free and exponential stability of the system. This approach allows the authors to compute simultaneously the two bounds that characterise the exponential stability rate of the solution by various efficient convex optimisation algorithms. Numerical examples are given to illustrate the effectiveness of the obtained results.

In this study, the problem of simultaneous estimation of system states and disturbances is addressed for two-dimensional (2D) linear systems. The considered 2D systems can be described as Fornasini–Marchesini second local state–space model coupled with unknown disturbances in the measurement equation. Asymptotically stable and uniformly ultimately bounded integrated state/disturbance observers are proposed as solutions to the simultaneous estimation problem under different system conditions. For the asymptotically stable integrated state/disturbance observer, a necessary and sufficient condition for its existence is presented and proved. For the uniformly ultimately bounded integrated state/disturbance observer, a sufficient condition for its existence is given and proved, and it can be designed such that its estimation error has arbitrarily small upper bound. Moreover, some constructive design methods are given for the proposed integrated state/disturbance observers. Finally, a thermal process plant and another numerical example are provided to illustrate the effectiveness of the proposed methods.

This study investigates the problem of event-triggered output-feedback ℋ_∞ control for networked control systems (NCSs) with non-uniform sampling. First, an event-triggered communication scheme is proposed, in which the output of the system is taken sample with a non-uniform sampling period, while whether or not the sampled data should be transmitted is determined by a predetermined well-designed event-triggering condition. Second, the event-triggered NCSs are modelled as a time-delay system, which regards the measured output-error between the output at the current sampling instant and the output at the last transmitted sampling instant. As a result, the stability and synthesis criteria are derived to guarantee the uniform ultimate bounded stability and the desired performance while using the less communication bandwidth. Finally, three illustrative examples are used to show the effectiveness of the proposed method.

This study deals with the problem of set-membership identification of non-linear-in-the-parameters models. To solve this problem, this study illustrates how the Bayesian approach can be used to determine the feasible parameter set (FPS) by assuming uniform distributed estimation error and flat model prior probability distributions. The key point of the methodology is the interval evaluation of the likelihood function and the result is a set of boxes with associated credibility indices. For each box, the credibility index is in the interval (0, 1] and gives information about the amount of consistent models inside the box. The union of the boxes with credibility value equal to one provides an inner approximation of the FPS, whereas the union of all boxes provides an outer estimation. The boxes with credibility value smaller than one are located around the boundary of the FPS and their credibility index can be used to iteratively refine the inner and outer approximations up to a desired precision. The main issues and performance of the developed algorithms are discussed and illustrated by means of examples.

In this study, the discrete-time antilinear systems with Markovian jumping parameters are investigated. The concept of stochastic stability is extended to the context of discrete-time Markovian jump (DTMJ) antilinear systems. By using stochastic Lyapunov approach, the authors derive some necessary and sufficient conditions for a DTMJ antilinear system to be stochastically stable in terms of coupled anti-Lyapunov matrix equations. In addition, two types of iterative algorithms are proposed to solve these coupled anti-Lyapunov matrix equations. Finally, some numerical examples are given to show the efficiency of the proposed algorithms and potential applications of the obtained results on antilinear systems.

In this study, the problem of model reduction based on balancing is investigated for both discrete- and continuous-time Markovian jump linear systems with partially unknown transition probabilities. By balancing transformation, the reduced-order model with the same structure as that of the original one is obtained by truncating the balanced model. For the obtain reduced order model, stability property is preserved under simultaneous balanced truncation. An upper bound of the model reduction error is guaranteed in the sense of a perturbation operator norm. Finally, two illustrative examples are provided to show the feasibility and effectiveness of the method presented in this study.

The digital filtering technology has been widely applied in a majority of signal processing applications. For the linear systems with state-space model, Kalman filter provides optimal state estimates in the sense of minimum-mean-squared errors and maximum-likelihood estimation. However, only with accurate system parameters and noise statistical properties, the estimation obtained by standard Kalman filter is the optimal state estimate. Most of time, the exact noise statistical properties could not be obtained as a priori information or even wrong statistical properties may be captured by the offline method. This may lead to a poor performance (even divergence) of Kalman filtering algorithm. In this study, a novel real-time filter, named as fast minimum norm filtering algorithm, has been proposed to deal with the case when the covariance matrices of the process and measurement noises were unknown in the linear time-invariant systems with state-space model. Tests have been performed on numerical examples to illustrate that the fast minimum norm filtering algorithm could be used to obtain acceptable precision state estimation in comparison with the standard Kalman filter for the discrete-time linear time-invariant systems.

Gait rehabilitation robots have potential for cardiovascular rehabilitation of patients with neurological deficits. A novel method was developed to guide exercise intensity by feedback control of oxygen uptake rate with a focus on tracking ramps as typically applied in maximal exercise testing. This approach is important as prior observations have noted a non-linear oxygen uptake response to increasing work rate, whereas a linear progression of exercise intensity is desirable. The proposed oxygen-uptake controller has embedded within it a human-in-the-loop feedback system for control of mechanical work rate which takes its target work rate from the automatic oxygen uptake control loop. Results of step and ramp tracking of target oxygen-uptake profiles, and disturbance rejection tests, demonstrated the technical feasibility and accuracy of the approach. Comparison with open-loop tests demonstrated clearly that the feedback system linearises the oxygen-uptake response and that linear progression of exercise intensity leads to higher peak oxygen uptake values. Further work will focus on clinical feasibility and the potential for cardiovascular rehabilitation in patients with neurological deficits.

The authors study causal dynamic source–channel codes for mean-square stabilisation of a linear plant with random initial state, over binary symmetric channels (BSCs). A binary expansion source coding scheme and two types of channel coding schemes are investigated: (i) dynamic repetition encoding under sequential majority logic decoding, and (ii) dynamic Fountain encoding under sequential BP decoding. The coding schemes are first analysed for an open-loop system, where the goal is to transmit a real-valued source over BSCs with the objective of minimising end-to-end mean-square error distortion. They derive upper- and lower bounds on the achievable distortion which is a function of time. Based on these distortion bounds, they show that the dynamic Fountain codes are able to stabilise (in mean-square sense) an unstable linear plant over BSCs.

In this study, the problem of iterative learning control (ILC) for discrete-time systems with quantised output measurements is considered. Here, a logarithmic quantiser is introduced and an ILC scheme is constructed by using output signals with only a finite number of quantisation levels. By using sector bound method to deal with the quantisation error, a learning condition of ILC that guarantees the convergence of tracking error is derived through rigorous analysis. It is shown that the convergence condition is determined by quantisation level, and the tracking error converges to a bound depending on quantisation density. Furthermore, the extension from linear systems to non-linear systems is also addressed. Finally, two illustrative examples are presented to demonstrate the theoretical results for both linear and non-linear systems.

An approximation-based decentralised adaptive fault compensation (FC) problem is addressed for large-scale non-linear time-delay systems with unknown faults in both time-delayed C ¹ non-linear interconnections and non-symmetric dead-zone actuators. Error surfaces constrained by prescribed performance bounds, which characterise the convergence rate and maximum overshoot of control errors, are presented to provide predefined bounds of control errors. Then, we design a memoryless decentralised FC control system using the constrained-surfaces-based dynamic surface design methodology, without constructing a dead-zone inverse and requiring the information about dead-zone parameters and time-delayed interactions. For the compensator design, the function approximation technique using neural networks is applied to adaptively estimate unknown non-linear effects and changes in model dynamics because of time-delayed interaction and dead-zone actuator faults. It is shown from Lyapunov stability theorem that all the error surfaces are preserved within the prescribed performance bounds and finally converge to an adjustable neighbourhood of the origin. Therefore guaranteed transient performance is achieved at the moment the faults occur.

This study presents an off-the-shelf error feedback controller that can completely rejects the sinusoidal disturbances whose magnitudes, phases, bias, frequencies and even the number of frequencies are all unknown. A closed-form solution is given under the assumptions that the plant has no uncertainty and has hyperbolic zero dynamics (i.e. there is no zero on the imaginary axis of the complex plane), and that the number of unknown frequencies has upper bound which is known. A non-minimum phase plant can be dealt with. The proposed controller is tested by a simulation, which verifies its effectiveness.