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.     

Robust H∞ filtering for switched linear discrete‐time systems with polytopic uncertainties

In this paper, the problem of robust H_∞ filtering for switched linear discrete‐time systems with polytopic uncertainties is investigated. Based on the mode‐switching idea and parameter‐dependent stability result, a robust switched linear filter is designed such that the corresponding filtering error system achieves robust asymptotic stability and guarantees a prescribed H_∞ performance index for all admissible uncertainties. The existence condition of such filter is derived and formulated in terms of a set of linear matrix inequalities (LMIs) by the introduction of slack variables to eliminate the cross coupling of system matrices and Lyapunov matrices among different subsystems. The desired filter can be constructed by solving the corresponding convex optimization problem, which also provides an optimal H_∞ noise‐attenuation level bound for the resultant filtering error system. A numerical example is given to show the effectiveness and the potential of the proposed techniques. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

Delay‐dependent H∞ performance analysis and filtering for Markovian jump systems with interval time‐varying delays

This paper investigates the problems of H_∞ disturbance attenuation and H_∞ filtering for Markovian jump systems with interval time‐varying delays. In terms of linear matrix inequalities, a less conservative delay‐range‐dependent H_∞ performance condition for Markovian jump systems is proposed by constructing a different Lyapunov–Krasovskii functional. The resulting criterion has advantages over some previous ones in that they involve fewer matrix variables, but has less conservatism. Based on this new condition, an improved H_∞ filtering algorithm is developed. Numerical examples are provided to demonstrate the efficiency and reduced conservatism of the results in this paper. Copyright © 2009 John Wiley & Sons, Ltd.     

自适应滑模控制具有状态和输入时滞的不确定系统

针对一类对象模型具有非匹配不确定性,且同时具有状态时滞和输入时滞的线性系统,基于LMI方法,提出了系统存在滑动模态时滞相关的充分条件,考虑到在处理输入时滞时引入了未知扰动,进一步设计了对扰动参数具有自适应估计能力自适应滑模控制器,该方法保证了闭环系统鲁棒渐近稳定。仿真结果进一步证实了该控制策略的可行性。     

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.     

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.     

Robust adaptive sliding mode control for uncertain time‐delay systems

This paper is devoted to robust adaptive sliding mode control for time‐delay systems with mismatched parametric uncertainties. Sufficient conditions for the existence of linear sliding surfaces are given in terms of linear matrix inequalities, by which the corresponding adaptive reaching motion controller is also designed. Simulation studies show the effectiveness of the control scheme. Copyright © 2008 John Wiley & Sons, Ltd.     

Sliding mode control of switched hybrid systems with time‐varying delay

This paper is concerned with the sliding mode control of a continuous‐time switched system with time‐varying delay in its state. By using the average dwell time approach and the piecewise Lyapunov function technique, a sufficient condition is first proposed to guarantee the exponential stability of the unforced system with the decay estimate explicitly given. A sufficient condition of the existence of a reduced‐order sliding mode dynamics is derived, and an explicit parametrization of the desired sliding surface is also given. The obtained conditions will be solved using the cone complementary linearization (CCL) method. An adaptive sliding mode controller for the reaching motion is then designed such that the trajectories of the resulting closed‐loop system can be driven onto a prescribed sliding surface and maintained there for all subsequent times. All the conditions obtained in this paper are delay dependent. Finally, two numerical examples are given to illustrate the effectiveness of the proposed theory. Copyright © 2008 John Wiley & Sons, Ltd.     

Adaptive reconfigurable control of systems with time‐varying delay against unknown actuator faults

This work is concerned with the problem of delay‐dependent adaptive fault‐tolerant controller design against unknown actuator faults for linear continuous systems with time‐varying delay. Based on the online estimation of possible faults by discontinuous adaptation law, identification parameters of the adaptive state feedback controller are updated autonomously to compensate the fault effects on the delayed system. For the first time, a convex combination idea and a projection‐type adaptive approach are combined organically to derive the main results. A set of new delay‐dependent reconfigurable stabilization criteria, which guarantee the stability of closed‐loop systems in both fault‐free and faulty cases, is established in terms of linear matrix inequalities. Two numerical instances for linear delayed systems and the linearized model for the lateral motion of Boeing 747 are respectively simulated to illustrate the superiority and the effectiveness of the presented adaptive delay‐dependent results. Copyright © 2013 John Wiley & Sons, Ltd.     

Output‐feedback H∞ quadratic tracking control of linear systems using reinforcement learning

This paper presents an online learning algorithm based on integral reinforcement learning (IRL) to design an output‐feedback (OPFB) H_∞ tracking controller for partially unknown linear continuous‐time systems. Although reinforcement learning techniques have been successfully applied to find optimal state‐feedback controllers, in most control applications, it is not practical to measure the full system states. Therefore, it is desired to design OPFB controllers. To this end, a general bounded L₂ ‐gain tracking problem with a discounted performance function is used for the OPFB H_∞ tracking. A tracking game algebraic Riccati equation is then developed that gives a Nash equilibrium solution to the associated min‐max optimization problem. An IRL algorithm is then developed to solve the game algebraic Riccati equation online without requiring complete knowledge of the system dynamics. The proposed IRL‐based algorithm solves an IRL Bellman equation in each iteration online in real time to evaluate an OPFB policy and updates the OPFB gain using the information given by the evaluated policy. An adaptive observer is used to provide the knowledge of the full states for the IRL Bellman equation during learning. However, the observer is not needed after the learning process is finished. A simulation example is provided to verify the convergence of the proposed algorithm to a suboptimal OPFB solution and the performance of the proposed method.     

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.     

Quantized H∞ filtering for state‐delayed systems with finite frequency specifications

This paper presents a novel design approach for the finite frequency (FF) H_∞ filtering problem for discrete‐time state‐delayed systems with quantized measurements. The system state and output are assumed affected by FF external noises. Attention is focused on the design of a stable filter that guarantees the stability and a prescribed ?₂ gain performance level for the filtering error system in the FF domain of input noises. Sufficient conditions for the solvability of this problem are developed by choosing an appropriate Lyapunov‐Krasovskii functional based on the delay partitioning technique and using the FF ?₂ gain definition combined with the generalized S‐procedure. Then, by means of Finsler's lemma, the derived conditions are linearized and additional slack variables are further introduced to more flexible result. Final filter design conditions are consequently established in terms of linear matrix inequalities in three different frequency ranges, ie, low‐, middle‐ and high‐frequency range. Finally, a simulation example is presented to illustrate the effectiveness and the merits of the proposed approach.     

Reliable H∞ filtering for discrete time‐delay Markovian jump systems with partly unknown transition probabilities

In this paper, the reliable H_∞ filtering problem is studied for a class of discrete nonlinear Markovian jump systems with sensor failures and time delays. The transition probabilities of the jumping process are assumed to be partly unknown. The failures of sensors are quantified by a variable taking values in a given interval. The time‐varying delay is unknown with given lower and upper bounds. The purpose of the addressed reliable H_∞ filtering problem is to design a mode‐dependent filter such that the filtering error dynamics is asymptotically mean‐square stable and also achieves a prescribed H_∞ performance level. By using a new Lyapunov–Krasovskii functional and delay‐partitioning technique, sufficient delay‐dependent conditions for the existence of such a filter are obtained. The filter gains are characterized in terms of the solution to a convex optimization problem that can be easily solved by using the semi‐definite programme method. A numerical example is provided to demonstrate the effectiveness of the proposed design approach. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptive output tracking for a class of non‐linear time‐delay systems

In this paper the output tracking control problem for a class of non‐linear time delay systems with some unknown constant parameters is addressed. Such a problem is solved in the case that the non‐linear time‐delay system has full delay relative degree and stable internal dynamics. It is supposed moreover that the output and its time derivatives until n?1, where n is the length of the state vector (euclidean part), do not depend explicitly on the unknown parameters. This work is the first step towards the application of the methodologies of adaptive control for non‐linear delayless systems, based on tools of differential geometry, to non‐linear time‐delay systems too. Copyright © 2004 John Wiley & Sons, Ltd.     

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.     

Mode‐independent H∞ filtering for discrete‐time Markov jump linear system with parametric uncertainties and quantized measurements

This paper is concerned with the problem of H_∞ filtering for discrete‐time Markov jump linear system with parametric uncertainties and quantized measurements, when the jumping mode information is not accessible. By converting the quantized errors into a sector‐bounded nonlinearity, the parametric uncertainties and measurements quantization are dealt with in a unified framework. The mode‐independent H_∞ filter is designed, and sufficient conditions are established via Lyapunov function approach, such that for all possible uncertain parameters and quantization errors, the resulting filtering error system is robustly stochastically stable and achieves a guaranteed H_∞ filtering error performance index. A numerical example is provided to demonstrate the feasibility and effectiveness of the proposed approach. Copyright © 2015 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.