Finite‐time H ∞ filtering for a class of discrete‐time Markovian jump systems with partly unknown transition probabilities

This paper is concerned with the problem of finite‐time H _∞ filtering for a class of Markovian jump systems subject to partial information on the transition probabilities. By introducing some slack matrix variables in terms of probability identity, a less conservative bounded real lemma is derived to ensure that filtering Markovian jump systems is finite‐time stable. Finally, the existence criterion of the desired filter is obtained such that the corresponding filtering error system is finite‐time bounded with a guaranteed H _∞ performance index. An example is given to illustrate the efficiency of the proposed method. Copyright © 2013 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.     

Fault detection filter design for discrete‐time switched linear systems with mode‐dependent average dwell‐time

This paper is concerned with the problem of the fault detection (FD) filter design for discrete‐time switched linear systems with mode‐dependent average dwell‐time. The switching law is mode‐dependent and each subsystem has its own average dwell‐time. The FD filters are designed such that the augmented switched systems are asymptotically stable, and the residual signal generated by the filters achieves a weighted l₂‐gain for some disturbances and guarantees an H _? performance for the fault. By the aid of multiple Lyapunov functions combined with projection lemma, sufficient conditions for the design of the FD filters are formulated by linear matrix inequalities, furthermore, the filters gains are characterized in terms of the solution of a convex optimization problem. Finally, an application to boost convertor is given to illustrate the effectiveness and the applicability of the proposed design method. Copyright © 2013 John Wiley & Sons, Ltd.     

Fault detection for a class of network‐based nonlinear systems with communication constraints and random packet dropouts

This paper is dealt with the fault detection (FD) problem for a class of network‐based nonlinear systems with communication constraints and random packet dropouts. The plant is described by a Takagi–Sugeno fuzzy time‐delay model, it has multiple sensors and only one of them is actually communicated with the FD filter at each transmission instant, and the packet dropouts occur randomly. The goal is to design a FD filter such that, for all unknown inputs, control inputs, time delays and incomplete data conditions, the estimation error between the residual and ‘fault’ (or, more generally, the weighted fault) is minimized. By casting the addressed FD problem into an auxiliary H_∞ filtering problem of a stochastic switched fuzzy time‐delay system, a sufficient condition for the existence of the desired FD filter is established in terms of linear matrix inequalities. A numerical example is provided to illustrate the effectiveness and applicability of the proposed technique. Copyright © 2011 John Wiley & Sons, Ltd.     

Online concurrent reinforcement learning algorithm to solve two‐player zero‐sum games for partially unknown nonlinear continuous‐time systems

Online adaptive optimal control methods based on reinforcement learning algorithms typically need to check for the persistence of excitation condition, which is necessary to be known a priori for convergence of the algorithm. However, this condition is often infeasible to implement or monitor online. This paper proposes an online concurrent reinforcement learning algorithm (CRLA) based on neural networks (NNs) to solve the H _∞ control problem of partially unknown continuous‐time systems, in which the need for persistence of excitation condition is relaxed by using the idea of concurrent learning. First, H _∞ control problem is formulated as a two‐player zero‐sum game, and then, online CRLA is employed to obtain the approximation of the optimal value and the Nash equilibrium of the game. The proposed algorithm is implemented on actor–critic–disturbance NN approximator structure to obtain the solution of the Hamilton–Jacobi–Isaacs equation online forward in time. During the implementation of the algorithm, the control input that acts as one player attempts to make the optimal control while the other player, that is, disturbance, tries to make the worst‐case possible disturbance. Novel update laws are derived for adaptation of the critic and actor NN weights. The stability of the closed‐loop system is guaranteed using Lyapunov technique, and the convergence to the Nash solution of the game is obtained. Simulation results show the effectiveness of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.     

Exponential l2 − l∞ filtering for discrete‐time switched systems under a new framework

In this paper, a robust exponential l₂ ? l_∞ filtering problem is addressed for discrete‐time switched systems with polytopic uncertainties. The purpose of robust exponential l₂ ? l_∞ filtering is to design a filter such that the resulting filtering error system is robustly exponentially stable with a decay rate and a prescribed exponential l₂ ? l_∞ performance index. The robust exponential l₂ ? l_∞ filtering problem is solved via an average dwell time approach. Sufficient conditions in terms of strict LMI are derived for checking the robust exponential stability of a filter. An explicit expression for the desired robust exponential filter is also given. Finally, a numerical example is provided to demonstrate the potential and effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

Network‐based fault detection for discrete‐time state‐delay systems: A new measurement model

In this paper, the fault detection problem is studied for a class of discrete‐time networked systems with multiple state delays and unknown input. A new measurement model is proposed to account for both the random measurement delays and the stochastic data missing (package dropout) phenomenon, which are typically resulted from the limited capacity of the communication networks. At any time point, one of the following cases (random events) occurs: measurement missing case, no time‐delay case, one‐step delay case, two‐step delay case, …, q‐step delay case. The probabilistic switching between different cases is assumed to obey a homogeneous Markovian chain. We aim to design a fault detection filter such that, for all unknown input and incomplete measurements, the error between the residual and weighted faults is made as small as possible. The addressed fault detection problem is first converted into an auxiliary H_∞ filtering problem for a certain Markovian jumping system (MJS). Then, with the help of the bounded real lemma of MJSs, a sufficient condition for the existence of the desired fault detection filter is established in terms of a set of linear matrix inequalities (LMIs). A simulation example is provided to illustrate the effectiveness and applicability of the proposed techniques. Copyright © 2007 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.     

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.     

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.     

Observer design for nonlinear parameter‐varying systems: Application to diesel engines

This paper deals with the problem of designing a nonlinear observer for diesel engines. The goal is to estimate the masses entering the cylinders and the inlet and exhaust pressures. To achieve this, the considered model subject to disturbances contains linear parameter‐varying part and nonlinear part having a large Lipschitz constant. The H _∞ criterion is used to reject the disturbances. Besides, the modified mean value theorem is applied to express the nonlinear error dynamics as a convex combination of known matrices with time‐varying coefficients. The sufficient conditions are derived and given in terms of linear matrix inequality. The advantage of the proposed method is that it can be applied to a wider class of nonlinear systems, particulary our case: diesel engines. The proposed approach is tested and evaluated using an advanced diesel engine professional simulator AMEsim (LMS International, Leuven, Belgium). Copyright © 2014 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.     

Fault detection for nonlinear networked systems with random packet dropout and probabilistic interval delay

In this paper, the fault detection (FD) problem of nonlinear networked control systems (NCSs) is investigated. A nonlinear stochastic systems model is proposed to account for the NCSs with network‐induced random packet dropout and non‐uniformly distributed time‐varying delay in both from sensor to controller and from controller to actuator. On the basis of the new model, by employing FD filter as residual generator, the addressed FD problem is converted into auxiliary nonlinear H _∞ filtering problem. Then, with the help of Lyapunov functional approach, a sufficient condition for the desired FD filter is constructed in terms of certain linear matrix inequalities, which depends on not only nonlinear level but also delay interval occurrence rate and successful joint packet transmission rate. Especially, a trade‐off phenomenon among maximum allowable delay bound, nonlinear level, and successful joint packet transmission rate is found, which typically resulted from the limited bandwidth of the communication networks. The effectiveness of the proposed methods is demonstrated by simulation examples. Copyright © 2011 John Wiley & Sons, Ltd.     

Multi‐objective optimization power control for code division multiple access systems

In code division multiple access (CDMA) communication systems, the communication channel is usually corrupted with time‐varying interferences, which include channel fading, multiple access interference, round‐trip delay, and noise. Power control is an important issue for CDMA systems to achieve higher communication link quality and better system capacity under time‐varying interferences. In the previous studies, most of power control algorithms only considered the user's target signal‐to‐interference‐and‐noise‐ratio (SINR) to maintain quality of service. In this study, a multi‐objective optimization method is proposed for power control design in CDMA systems. With a shadow system and an h _∞ filter to compensate for the round‐trip delay, the proposed power control scheme can simply adjust transmission power to achieve the best compromise between several objectives, such as minimization of SINR deviation, minimization of power consumption, and minimization of the system outage. Several simulation results are given to confirm the performance of the proposed power control scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Harmonic fold back reduction at the N‐path filters

In this paper, a method is proposed to reduce harmonic fold back (HFB) problem of N‐path filters, without increasing the input reference clock (f_CLK ) frequency. The HFB at the N‐path filter is analyzed, and simple expressions are extracted to model this problem. Using the results of the analysis, an M‐of‐N‐path filter has been proposed that behaves like an M × N‐path filter in terms of HFB problem; however, the f_CLK frequency of this structure is the same as an N‐path filter. To demonstrate the feasibility of the proposed idea, a 3‐of‐4‐path filter is designed, and its characteristics are compared with 4‐path and 12‐path filters by simulation. Impacts of different non‐idealities like clock‐phase error, mismatch, and parasitic capacitance are investigated. The transistor‐level implementation of this filter is performed in 0.18 µm Complementary Metal Oxide Semiconductor (CMOS) technology. The simulation results show that the filter has the pass‐band gain of 17 dB, tuning range of 0.2–1.2 GHz, −3 dB bandwidth of 25 MHz, quality factor of 8–48, 18 dB out‐of‐band rejection, 16 dB rejection of the third harmonic of switching frequency (f_s ), and the noise figure of 4.35 dB (using ideal G_m cells) and 6.95 dB (for practical G_m cells). The strongest harmonic folding to the filter pass‐band occurs around 11f_s with the attenuation of 23.8 dB. Each G_m cell draws about 12.4 mA from 1.8 V supply, and the out‐of‐band IIP3 and P _{1 dB,CP} are 17 and 4 dBm, respectively. Copyright © 2016 John Wiley & Sons, Ltd.     

Constructive approximation of non‐linear discrete‐time systems

It is known that large classes of approximately‐finite‐memory maps can be uniformly approximated arbitrarily well by the maps of certain non‐linear structures. As an application, it was proved that time‐delay networks can be used to uniformly approximate arbitrarily well the members of a large class of causal nonlinear dynamic discrete‐time input–output maps. However, the proof is non‐constructive and provides no information concerning the determination of a structure that corresponds to a prescribed bound on the approximation error. Here we give some general results concerning the problem of finding the structure. Our setting is as follows. There is a large family 𝒢 of causal time‐invariant approximately‐finite‐memory input‐output maps G from a set S of real d‐vector‐valued discrete‐time inputs (with d⩾1) to the set of ℝ‐valued discrete‐time outputs, with both the inputs and outputs defined on the non‐negative integers 𝒵₊. We show that for each ϵ>0, any Gϵ𝒢 can be uniformly approximated by a structure map H(G, ·) to within tolerance ϵ, and we give analytical results and an example to illustrate how such a H(G, ·) can be determined in principle. Copyright © 2000 John Wiley & Sons, Ltd.     

Adaptive parallel simultaneous stabilization of a set of uncertain port‐controlled hamiltonian systems subject to actuator saturation

This paper investigates adaptive parallel simultaneous stabilization (APSS) of a set of uncertain nonlinear port‐controlled Hamiltonian (PCH) systems subject to actuator saturation and proposes a number of results on the design of the APSS controllers. First, the case of two PCH systems is studied. Using both the dissipative Hamiltonian structural and saturated actuator properties, the two systems are combined to generate an augmented PCH system, with which, some results on the control designs are then obtained. When there are external disturbances in the two systems, an H _∞ APSS controller is designed for the systems. Second, the case of more than two uncertain PCH systems subject to actuator saturation is investigated, and several new results are proposed for the APSS problem. Finally, an illustrative example is presented to show that the adaptive stabilization controllers obtained in this paper work very well. Copyright © 2013 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.