Adaptive finite‐time control for nonlinear teleoperation systems with asymmetric time‐varying delays

This paper addresses the adaptive finite‐time control problem of nonlinear teleoperation system in the presence of asymmetric time‐varying delays. To achieve the finite‐time position tracking, a novel adaptive finite‐time coordination algorithm based on subsystem decomposition is developed. By introducing a switching‐technique‐based error filtering into our design framework, the complete closed‐loop master (slave) teleoperation system is modeled as a special class of switched system, which is composed of two subsystems. To analyze such system, a finite‐time state‐independent input‐to‐output stability criterion is first developed for some normal switched nonlinear delayed systems. Then based on the classical Lyapunov–Krasovskii method, the stability of complete closed‐loop systems is obtained. It is shown that the proposed scheme can make the position errors converge into a deterministic domain in finite time when the robots continuously contact with human operator and/or the environment in the presence of asymmetric time‐varying delays. Finally, the simulation results are given to demonstrate the effectiveness. Copyright © 2015 John Wiley & Sons, Ltd.     

Finite‐time control for LPV systems with parameter‐varying time delays and exogenous disturbances

In this paper, we consider the stability analysis and control synthesis of finite‐time boundedness problems for linear parameter‐varying (LPV) systems subject to parameter‐varying time delays and external disturbances. First, the concepts of uniform finite‐time stability and uniform finite‐time boundedness are introduced to LPV systems. Then, sufficient conditions, which guarantee LPV systems with parameter‐varying time delays finite‐time bounded, are presented by using parameter‐dependent Lyapunov–Krasovskii functionals and free‐weight matrix technologies. Moreover, on the basis of the results on the uniform finite‐time boundedness, the parameter‐dependent state feedback controllers are designed to finite‐time stabilize LPV systems. Both analysis and synthesis conditions are delay‐dependent, and they are formulated in terms of linear matrix inequalities by using efficient interior‐point algorithms. Finally, results obtained in simulation demonstrate the effectiveness of the proposed approach. Copyright © 2017 John Wiley & Sons, Ltd.     

On reachable set estimation of two‐dimensional systems described by the Roesser model with time‐varying delays

In this paper, the problem of reachable set estimation of two‐dimensional (2‐D) discrete‐time systems described by the Roesser model with interval time‐varying delays is considered for the first time. New 2‐D weighted summation inequalities, which provide a tighter lower bound than the commonly used Jensen summation inequality, are proposed. Based on the Lyapunov‐Krasovskii functional approach, and by using the 2‐D weighted summation inequalities presented in this paper, new delay‐dependent conditions are derived to ensure the existence of an ellipsoid that bounds the system states in the presence of bounded disturbances. The derived conditions are expressed in terms of linear matrix inequalities, which can be solved by various computational tools to determine a smallest possible ellipsoidal bound. Applications to exponential stability analysis of 2‐D systems with delays are also presented. The effectiveness of the obtained results are illustrated by numerical examples.     

Adaptive fault‐tolerant time‐varying formation tracking for multiagent systems with multiple leaders

In this paper, an adaptive fault‐tolerant time‐varying formation control problem for nonlinear multiagent systems with multiple leaders is studied against actuator faults and state‐dependent uncertainties. Simultaneously, the followers form a predefined formation while tracking reference signal determined by the convex combination of the multiple leaders. Based on the neighboring relative information, an adaptive fault‐tolerant formation time‐varying control protocol is constructed to compensate for the influences of actuator faults and model uncertainties. In addition, the updating laws can be adjusted online through the adaptive mechanism, and the proposed control protocol can guarantee that all the signals in the closed‐loop systems are bounded. Lyapunov‐like functions are addressed to prove the stability of multiagent systems. Finally, two examples are provided to demonstrate the effectiveness of the theoretical results.     

Observer‐based fault diagnosis and self‐restore control for systems with measurement delays

The problems of fault diagnosis and fault‐tolerant control are considered for systems with measurement delays. In contrast to the present fault diagnosis and fault‐tolerant control approaches, which consider only the input delay and/or state delay, the main contribution of this paper consists of proposing a new observer‐based reduced‐order fault diagnoser construction approach and a design approach to dynamic self‐restore fault‐tolerant control law for systems with measurement delays. First, the time‐delay system is transformed into a delay‐free system in form by a special functional‐based delay‐free transformation approach for measurement delays. Then, the fault diagnosis is realized online via the proposed reduced‐order fault diagnoser. Using the results of fault diagnosis, two dynamic self‐restore control laws are designed to make the system isolated from faults. A numerical example demonstrates the feasibility and validity of the proposed scheme. © 2012 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Compensation of time‐varying input delay for discrete‐time nonlinear systems

We consider general discrete‐time nonlinear systems (of arbitrary nonlinear growth) with time‐varying input delays and design an explicit predictor feedback controller to compensate the input delay. Such results have been achieved in continuous time, but only under the restriction that the delay rate is bounded by unity, which ensures that the input signal flow does not get reversed, namely, that old inputs are not felt multiple times by the plant (because on such subsequent occasions, the control input acts as a disturbance). For discrete‐time systems, an analogous restriction would be that the input delay is non‐increasing. In this work, we do not impose such a restriction. We provide a design and a global stability analysis that allow the input delay to be arbitrary (containing intervals of increase, decrease, or stagnation) over an arbitrarily long finite period of time. Unlike in the continuous‐time case, the predictor feedback law in the discrete‐time case is explicit. We specialize the result to linear time‐invariant systems and provide an explicit estimate of the exponential decay rate. Carefully constructed examples are provided to illustrate the design and analytical challenges. Copyright © 2015 John Wiley & Sons, Ltd.     

Stabilization of nonlinear uncertain systems with stochastic actuator failures and time‐varying delay

In this paper, we investigate the adaptive state‐feedback stabilization problem for a class of nonlinear systems subject to parametric uncertainties, time‐varying delay, and Markovian jumping actuator failures. First, some fundamental results, including the infinitesimal generator and conditions for the existence and uniqueness of the solution, are established for nonlinear systems w.r.t. Markovian vector and time‐varying delay. Subsequently, corresponding stability criterion is generalized to the considered systems. By employing the backstepping method and the tuning function technique, a systematic adaptive fault‐tolerant control scheme is proposed, which guarantees the boundedness in probability of all the closed‐loop signals. It is noted that no fault detection and diagnostic block are needed, and the control law can be adapted automatically by taking account of the innovative state information. The efficiency of the designed controller is demonstrated by an illustrative example. Copyright © 2015 John Wiley & Sons, Ltd.     

New results of stability analysis for systems with time‐varying delay

This paper studies the problem of stability analysis for continuous‐time systems with time‐varying delay. By developing a delay decomposition approach, the information of the delayed plant states can be taken into full consideration, and new delay‐dependent sufficient stability criteria are obtained in terms of linear matrix inequalities. The merits of the proposed results lie in their less conservatism, which are realized by choosing different Lyapunov matrices in the decomposed integral intervals and estimating the upper bound of some cross term more exactly. Numerical examples are given to illustrate the effectiveness and less conservatism of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.     

Exponential stability of impulsive positive switched systems with discrete and distributed time‐varying delays

This paper studies the exponential stability problems of discrete‐time and continuous‐time impulsive positive switched systems with mixed (discrete and distributed) time‐varying delays, respectively. By constructing novel copositive Lyapunov‐Krasovskii functionals and using the average dwell time technique, delay‐dependent sufficient conditions for the solvability of considered problems are given in terms of fairly simple linear matrix inequalities. Compared with the most existing results, by introducing an extra real vector, restrictive conditions on derivative of the time‐varying delays (less than 1) are relaxed, thus the obtained improved stability criteria can deal with a wider class of continuous‐time positive switched systems with time‐varying delays. Finally, two simple examples are provided to verify the validity of theoretical results.     

Integrated fault detection system design for linear discrete time‐varying systems with bounded power disturbances

This paper investigates the problem of an integrated fault detection system design for linear discrete time‐varying systems with bounded power disturbances. In the integrated design of residual generator and evaluator, an approximated energy constraint is first imposed on the bounded power disturbances, and then selected by solving a min–max problem to achieve minimal‐size set of undetectable faults under the condition of zero false alarms. To tackle the problem that the computational burden involved in solving the min–max optimization grows with time, the moving horizon method is proposed. The proposed approach in this paper has two advantages: (i) the approximated energy constraint on bounded power disturbances is explicitly selected as a min–max solution in the integrated design to improve fault detection rate; by contrast, when directly applying any existing fault detection method to the case of bounded power disturbances, a predefined approximated energy constraint is implicitly introduced without considering fault detection performance; (ii) the design objective of the proposed approach can choose to consider faults only in the recent time horizon rather than faults in the complete time horizon; this strategy enhances detection performance of recent faults and benefits early fault detection, but has not been considered by existing fault detection methods. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive quantized tracking control for uncertain switched nonstrict‐feedback nonlinear systems with discrete and distributed time‐varying delays

This paper is concerned with an adaptive tracking problem for a more general class of switched nonstrict‐feedback nonlinear time‐delay systems in the presence of quantized input. The system structure in a nonstrict‐feedback form, the discrete and distributed time‐varying delays, the sector‐bounded quantized input, and arbitrary switching behavior are involved in the considered systems. In particular, to overcome the difficulties from the distributed time‐varying delays and the sector‐bounded quantized input, the mean‐value theorem for integrals and some special techniques are exploited respectively. Moreover, by combining the Lyapunov‐Razumikhin method, dynamic surface control technique, fuzzy logic systems approximation, and variable separation technique, a quadratic common Lyapunov function is easily built for all subsystems and a common adaptive quantized control scheme containing only 1 adaptive parameter is proposed. It is shown that the tracking error converges to an adjustable neighborhood of the origin whereas all signals of the closed‐loop systems are semiglobally uniformly ultimately bounded. Finally, 2 simulation examples are provided to verify the feasibility and effectiveness of the proposed design methodology.     

Delay‐dependent passivity and passification for uncertain Markovian jump systems with time‐varying delays

This paper deals with the problems of passivity analysis and passivity‐based controller design for Markovian jump systems with both time‐varying delays and norm‐bounded parametric uncertainties. Firstly, new delay‐dependent conditions for the considered system to be passive are obtained by using a mode‐dependent Lyapunov functional and by introducing some slack variables. These conditions are expressed by means of LMIs that are easy to check. It is shown through a numerical example that the obtained passivity conditions are less conservative than the existing ones in the literature. Secondly, the passification problem is investigated. On the basis of the obtained passivity conditions, dynamic output‐feedback controllers are designed, which ensure that the resulting closed‐loop system is passive. The effectiveness of the proposed design method is demonstrated by a numerical example. Copyright © 2011 John Wiley & Sons, Ltd.     

New stability criterion for linear switched systems with time‐varying delay

This paper studies the stability problem of a class of linear switched systems with time‐varying delay in the sense of Hurwitz convex combination. By designing a parameter‐dependent switching law and using a new convex combination technique to deal with delay terms, a new stability criterion is established in terms of LMIs, which is dependent on the parameters of Hurwitz convex combination. The advantage of the new criterion lies in its less conservatism and simplicity. Numerical examples are given to illustrate the effectiveness and the less conservatism of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

A new result on the delay‐dependent stability of discrete systems with time‐varying delays

This paper proposes an improvement to the delay‐dependent stability of discrete systems with time‐varying delays. The approach is based on the observation that the positive definiteness of a chosen Lyapunov–Krasovskii functional does not necessarily require all the involved symmetric matrices to be positive definite, which has been overlooked in the literature. The derived delay‐dependent stability conditions are in terms of linear matrix inequalities. It is theoretically proved that our results are less conservative than the corresponding ones obtained by requiring the positive definiteness of all the symmetric matrices in a chosen Lyapunov–Krasovskii functional. The importance of the present approach is that a great number of delay‐dependent analysis and synthesis results obtained by the aforementioned requirement in the literature can be improved by the present approach without introducing any new decision variables. Copyright © 2013 John Wiley & Sons, Ltd.     

Robust delay‐dependent guaranteed cost controller design for uncertain nonlinear neutral systems with time‐varying state delays

In this paper, the problem of robust delay‐dependent guaranteed cost control for uncertain nonlinear neutral systems with time‐varying state delay is investigated. The control law is chosen to be a memoryless type one. Neither any model transformation nor bounding of any cross terms are utilized. The system under consideration may be subjected to both norm‐bounded uncertainties and nonlinear parameter perturbations. A delay‐dependent sufficient condition is obtained in terms of a matrix inequality for which a cone complementarity problem is introduced to provide a feasible solution set. Two numerical examples have been demonstrated to show the effective application of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.     

Global adaptive stabilization for high‐order uncertain time‐varying nonlinear systems with time‐delays

This paper focuses on the adaptive stabilization problem for a class of high‐order nonlinear systems with time‐varying uncertainties and unknown time‐delays. Time‐varying uncertain parameters are compensated by combining a function gain with traditional adaptive technique, and unknown multiple time‐delays are manipulated by the delicate choice of an appropriate Lyapunov function. With the help of homogeneous domination idea and recursive design, a continuous adaptive state‐feedback controller is designed to guarantee that resulting closed‐loop systems are globally uniformly stable and original system states converge to zero. The effectiveness of the proposed control scheme is illustrated by the stabilization of delayed neural network systems. Copyright © 2016 John Wiley & Sons, Ltd.     

BIBO stability and stabilization of networked control systems with short time‐varying delays

This paper presents a robust control approach to solve the stability and stabilization problems for networked control systems (NCSs) with short time‐varying delays. A new discrete‐time linear uncertain system model is proposed to describe the NCS, and the uncertainty of the network‐induced delay is transformed into the uncertainty of the system matrix. Based on the obtained uncertain system model, a sufficient BIBO stability condition for the closed‐loop NCS is derived by applying the small gain theorem. The obtained stability condition establishes a quantitative relation between the BIBO stability of the closed‐loop NCS and two delay parameters, namely, the delay upper bound and the delay variation range bound. Moreover, design procedures for the state feedback stabilizing controllers are also presented. An illustrative example is provided to demonstrate the effectiveness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

Finite‐time stabilization for a class of nonlinear systems with time‐varying delay

This paper investigates the finite‐time stabilization problem for a class of nonlinear systems with time‐varying delay. Under suitable assumptions, a new state feedback control law is designed by using the adding a power integrator technique. By constructing an appropriate Lyapunov‐Krasovskii functional, it is shown that the corresponding closed‐loop system is finite‐time stable. Two simulation examples are given to verify the effectiveness of the proposed scheme.