On robust H∞ filtering of uncertain Markovian jump time‐delay systems

This paper is concerned with the problems of stability analysis, H_∞ performance analysis, and robust H_∞ filter design for uncertain Markovian jump linear systems with time‐varying delays. The purpose is to improve the existing results on these problems. Firstly, a new delay‐dependent stability criterion is obtained on the basis of a novel mode‐dependent Lyapunov functional. Secondly, a new delay‐dependent bounded real lemma (BRL) is derived. It is shown that the presented stability criterion and the BRL are less conservative than the existing ones in the literature. Thirdly, with the new BRL, delay‐dependent conditions for the solvability of the addressed H_∞ filtering problem are given. All the results obtained in this paper are expressed by means of strict linear matrix inequalities. Three numerical examples are provided to demonstrate the utility of the proposed methods. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust adaptive tracking control of uncertain discrete time systems

In this paper, the problem of robust adaptive tracking for uncertain discrete‐time systems is considered from the slowly varying systems point of view. The class of uncertain discrete‐time systems considered is subjected to both 𝓁_∞ to 𝓁_∞ bounded unstructured uncertainty and external additive bounded disturbances. A priori knowledge of the dynamic model of the reference signal to be tracked is not completely known. For such problem, an indirect adaptive tracking controller is obtained by frozen‐time controllers that at each time optimally robustly stabilize the estimated models of the plant and minimize the worst‐case steady‐state absolute value of the tracking error of the estimated model over the model uncertainty. Based on 𝓁_∞ to 𝓁_∞ stability and performance of slowly varying system found in the literature, the proposed adaptive tracking scheme is shown to have good robust stability. Moreover, a computable upper bound on the size of the unstructured uncertainty permitted by the adaptive system and a computable tight upper bound on asymptotic robust steady‐state tracking performance are provided. Copyright © 2005 John Wiley & Sons, Ltd.     

H∞ filtering for continuous‐time singular systems with time‐varying delay

This paper focuses on H_∞ filter design for continuous‐time singular systems with time‐varying delay. A delay‐dependent H_∞ performance analysis result is first established for error systems via a novel estimation method. By combining a well‐known inequality with a delay partition technique, the upper bound of the derivative of the Lyapunov functional is estimated more tightly and expressed as a convex combination with respect to the reciprocal of the delay rather than the delay. Based on the derived H_∞ performance analysis results, a regular and impulse‐free H_∞ filter is designed in terms of linear matrix inequalities (LMIs). A numerical example is given to demonstrate the merits of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

Teaching sampled‐data H∞ control theory using arm robot experiment system

This paper explains how to use an arm robot experiment system to teach sampled‐data H_∞ control theory. A design procedure is presented for a digital tracking control system for a continuous plant with structured uncertainties; the target is the positioning control of an arm robot. To guarantee the robust stability of the closed‐loop system and provide the desired closed‐loop performance, the design problem is first formulated as a sampled‐data H_∞ control problem, and is then transformed into an equivalent discrete‐time H_∞ control problem. Finally, linear matrix inequalities are used to obtain a reduced‐order output‐feedback controller and a static state‐feedback controller. In a course, the design procedure is explained and practice is provided through simulations and experiments. © 2011 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Robust learning controller design for MIMO stochastic discrete‐time systems: An H∞‐based approach

This paper is devoted to designing iterative learning control (ILC) for multiple‐input multiple‐output discrete‐time systems that are subject to random disturbances varying from iteration to iteration. Using the super‐vector approach to ILC, statistical expressions are presented for both expectation and variance of the tracking error, and time‐domain conditions are developed to ensure their asymptotic stability and monotonic convergence. It shows that time‐domain conditions can be tied together with an H_∞‐based condition in the frequency domain by considering the properties of block Toeplitz matrices. This makes it possible to apply the linear matrix inequality technique to describe the convergence conditions and to obtain formulas for the control law design. Furthermore, the H_∞‐based approach is shown applicable to ILC design regardless of the system relative degree, which can also be used to address issues of model uncertainty. For a class of systems with a relative degree of one, simulation tests are provided to illustrate the effectiveness of the H_∞‐based approach to robust ILC design. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust adaptive H∞ control design for heart rate regulation during rhythmic exercises of unknown type

The aim of the study is to regulate the human heart rate (HR) response to a predefined reference profile during aerobic activities of unknown type. A novel feature of the designed control system is obtained to generate the desired rhythmic movements, which is required to achieve the target HR profile during aerobic activities of unknown type. These rhythmic movements or frequency of locomotion is known as the exercise rate (ER) and is quantified as a fundamental measure of exercise intensity. The relationship between ER and HR is modeled by using a linear time‐varying system. The parameters of the model are estimated using a Kalman filter. Based on this model, a robust adaptive H_∞ controller is designed. The H_∞ controller generates target ER (ER_T) corresponding to target HR (HR_T). This ER_T is communicated to the exercising subject by using a human actuating system (HAS). The role of HAS is to achieve ER_T. To validate the performance of the system, it is tested on six healthy subjects during rowing and cycling exercises. The results demonstrate that the designed control system can regulate HR at a given profile with an average root mean square error of 3.1857 bpm and 2.9396 bpm for rowing and cycling, respectively. The developed system can be used for designing an optimal exercising protocol for individuals.     

Adaptive internal model control: the discrete‐time case

This paper considers the design and analysis of a discrete‐time H₂ optimal robust adaptive controller based on the internal model control structure. The certainty equivalence principle of adaptive control is used to combine a discrete‐time robust adaptive law with a discrete‐time H₂ internal model controller to obtain a discrete‐time adaptive H₂ internal model control scheme with provable guarantees of stability and robustness. The approach used parallels the earlier results obtained for the continuous‐time case. Nevertheless, there are some differences which, together with the widespread use of digital computers for controls applications, justifies a separate exposition. Copyright © 2001 John Wiley & Sons, Ltd.     

Delay‐dependent model reduction for continuous‐time switched state‐delayed systems

This paper studies the problem of exponential H_∞ model reduction for continuous‐time switched delay system under average dwell time (ADT) switching signals. Time delay under consideration is interval time varying. Our attention is focused on the construction of the desired reduced order models, which guarantee that the resulting error systems under ADT switching signals are exponentially stable with an H_∞ norm bound. By introducing a block matrix and making use of the ADT approach, delay‐dependent sufficient conditions for the existence of reduced order models are derived and formulated in terms of strict linear matrix inequalities (LMIs). Owing to the absence of non‐convex constraints, it is tractable to construct an admissible reduced order model. The effectiveness of the proposed methods is illustrated via two numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.     

Passivity‐based parameterized adaptive disturbance attenuation controller design for switched polynomial nonlinear systems

This paper is concerned with the adaptive disturbance attenuation control problem for a class of switched polynomial nonlinear systems. At first, a parameterized controller is designed to transform the switched polynomial nonlinear systems into switched Hamiltonian systems with polynomial structure. Then, combining with the solve‐parameter algorithm described in this paper, a mixed adaptive passivity and H₂/H_∞ control method is devoted. Comparing with the existing results, the obtained adaptive disturbance attenuation controller has better performance. Finally, a numerical example is given to illustrate the effectiveness of the proposed methods.     

Neural‐network‐based finite‐time H∞ control for extended Markov jump nonlinear systems

This paper presents a neural‐network‐based finite‐time H_∞ control design technique for a class of extended Markov jump nonlinear systems. The considered stochastic character is described by a Markov process, but with only partially known transition jump rates. The sufficient conditions for the existence of the desired controller are derived in terms of linear matrix inequalities such that the closed‐loop system trajectory stays within a prescribed bound in a fixed time interval and has a guaranteed H_∞ noise attenuation performance for all admissible uncertainties and approximation errors of the neural networks. A numerical example is used to illustrate the effectiveness of the developed theoretic results. Copyright © 2009 John Wiley & Sons, Ltd.     

Towards a performance theory of robust adaptive control

We consider standard robust adaptive control designs based on the dead‐zone and projection modifications, and compare their performance w.r.t. a worst case transient cost functional penalizing the ??^∞ norm of the output, control and control derivative. If a bound on the ??^∞ norm of the disturbance is known, it is shown that the dead‐zone controller outperforms the projection controller if the a priori information on the uncertainty level is sufficiently conservative. The second result shows that the projection controller is superior to the dead‐zone controller when the a priori information on the disturbance level is sufficiently conservative. For conceptual clarity the results are presented on a non‐linear scalar system with a single uncertain parameter and generalizations are briefly discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

Robust H∞ filtering for uncertain Markovian jump systems with mode‐dependent distributed delays

This paper deals with the problem of robust H_∞ filter design for Markovian jump systems with norm‐bounded time‐varying parameter uncertainties and mode‐dependent distributed delays. Both the state and the measurement equations are assumed to be with distributed delays. Sufficient conditions for the existence of robust H_∞ filters are obtained. Via solving a set of linear matrix inequalities, a desired filter can be constructed. The developed theory is illustrated by a simulation example. Copyright © 2009 John Wiley & Sons, Ltd.     

LMI solutions to the mixed ℋ︁−/ℋ︁∞ fault detection observer design for linear parameter‐varying systems

This paper addresses the mixed ??_?/??_∞ fault detection observer design issue for a class of linear parameter‐varying (LPV) systems. Analogous to the definition of the quadratic ??_∞ performance for LPV systems and the ??_? index for linear time invariant (LTI) systems, the quadratic ??_? index and the affine quadratic ??_? index for LPV systems are defined in terms of linear matrix inequalities (LMIs). The first algorithm for designing the mixed ??_?/H_∞ observer is proposed, which aims at minimizing the quadratic ??_∞ performance and maximizing the quadratic ??_? index of the observer error dynamic systems. To reduce the conservativeness of this algorithm, the affine quadratic ??_∞ performance and the affine ??_? index for LPV systems are utilized. The robustness conditions and affine ??_? index conditions for the underlying observer optimization issue are formulated as parameter‐dependent LMIs. The Gridding technique and multi‐convexity concept are applied, respectively, for reducing the parameter‐dependent LMIs to finite LMI constraints. Correspondingly, two iterative algorithms are proposed. Furthermore, the threshold design and the estimation of the worst undetectable fault size are investigated. An example is studied to demonstrate the effectiveness of the proposed algorithms. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust H ∞ filtering for a class of uncertain stochastic hybrid neutral systems with time‐varying delay

This paper is devoted to the problem of robust H _∞ filtering for a class of uncertain switched neutral systems subject to stochastic disturbance and time‐varying delay. Attention is focused on the design of a full‐order switched filter such that the filtering error system is robust mean‐square exponentially stable with a prescribed weighted H _∞ performance. On the basis of the average dwell time approach and the piecewise Lyapunov function technique, sufficient conditions for the solvability of this problem are obtained in terms of linear matrix inequalities. Then, by solving the corresponding linear matrix inequalities, the desired full‐order switched filter is derived for all admissible uncertainties, time‐varying delay, and stochastic disturbances. A numerical example is given to illustrate the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

Stability and H∞ performance of multiple‐delay systems with successive delay components

This paper presents a new model for linear time‐delay systems with multiple delayed states where each delay contains finite number of successive components with different time‐varying properties, referred to as multiple‐delay system with successive time‐varying delay components (MDSSTDCs). General stability result and H_∞ performance conditions, under which the MDSSTDCs are asymptotically stable with certain H_∞ disturbance attenuation level, are derived by exploiting a general Lyapunov–Krasovskii functional and by making use of novel techniques for time‐delay systems. The result is applied to two special types of time‐delay systems frequently used in engineering applications and corresponding conditions for stability and H_∞ performance are obtained. Copyright © 2010 John Wiley & Sons, Ltd.     

Prescribed performance adaptive fuzzy dynamic surface control of nonaffine time‐varying delayed systems with unknown control directions and dead‐zone input

In this paper, an adaptive prescribed performance control method is presented for a class of uncertain strict feedback nonaffine nonlinear systems with the coupling effect of time‐varying delays, dead‐zone input, and unknown control directions. Owing to the universal approximation property, fuzzy logic systems are used to approximate the uncertain terms in the system. Since there is no systematic approach to determine the required upper bounds of errors in control systems, the prior selection of control parameters to have a satisfactory performance is somehow impossible. Therefore, the prescribed performance technique as a solution is applied in this study to bring satisfactory performance indices to the system such as overshoot and steady state performance within a predetermined bound. Dynamic surface control strategy is also introduced to the proposed control scheme to address the “explosion of complexity” behavior existing in conventional backstepping methods. To ease the control design, the mean‐value theorem is utilized to transform the nonaffine system into the affine one. Moreover, with the help of this theorem, the unknown dead‐zone nonlinearity is separated into the linear and nonlinear disturbance‐like bounded term. The proposed method relaxes a prior knowledge of control direction by employing Nussbaum‐type functions, and the effect of time‐varying delays are compensated by constructing the proper Lyapunov‐Krasovskii functions. The proposed controller guarantees that all the closed‐loop signals are semiglobally uniformly ultimately bounded and the error evolves within the decaying prescribed bounds. In the end, in order to demonstrate the superiority of this method, simulation examples are given.     

A new model reference adaptive control for linear time‐varying systems

Recent results on the adaptive control of linear time‐varying systems have considered mostly the case in which the range or rate of parameter variations is small. In this paper, a new state feed‐back model reference adaptive control is developed for systems with bounded arbitrary parameter variations. The important feature of the proposed adaptive control is an uncertainty estimation algorithm, which guarantees almost zero tracking error. Note that the conventional parameter estimation algorithm in the adaptive control guarantees only bounded tracking error. Copyright © 2000 John Wiley & Sons, Ltd.     

Adaptive control design for uncertain polynomial nonlinear systems with parametric uncertainties

In this paper, we will develop an adaptive ??_∞ control approach for a class of polynomial nonlinear systems with parametric uncertainties. Motivated by the dissipation theory and the vector projection technique, we propose a nonlinear adaptive ??_∞ controller and its associated parameter adaptation law. The proposed adaptive control strategy is capable of identifying unknown parameter values quickly and minimizing the effect of estimation error. To further improve adaptive controlled performance, the Lyapunov function will be relaxed from quadratic to higher‐order forms and the controller gains are generalized from constant to parameter‐dependent. All of the synthesis conditions are formulated in the framework of polynomial/constant linear matrix inequalities and solvable using available software packages. Copyright © 2010 John Wiley & Sons, Ltd.     

Delay‐dependent robust L2–L∞ filtering of T‐S fuzzy systems with time‐varying delays

This paper considers the problem of robust delay‐dependent L₂–L_∞ filtering for a class of Takagi–Sugeno fuzzy systems with time‐varying delays. The purpose is to design a fuzzy filter such that both the robust stability and a prescribed L₂–L_∞ performance level of the filtering error system are guaranteed. A delay‐dependent sufficient condition for the solvability of the problem is obtained and a linear matrix inequality (LMI) approach is developed. A desired filter can be constructed by solving a set of LMIs. Copyright © 2009 John Wiley & Sons, Ltd.