Simultaneous time‐varying actuator and sensor fault reconstruction based on PI observer for LPV systems

We consider problems of actuator and sensor fault reconstruction simultaneously for linear parameter varying systems expressed in polytopic forms. By extending the sensor fault as an auxiliary state, a polytopic unknown input proportional‐integral observer in which the actuator fault signals are assumed to be time varying is developed to estimate the system states and the actuator and sensor fault at the same time. The existence conditions of the observer are derived in terms of linear matrix inequalities that can be readily handled via some efficient tools. An example is given to demonstrate the advantages of the proposed method in comparison to the existing results. Copyright © 2014 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.     

Less conservative criteria for fault accommodation of time‐varying delay systems using adaptive fault diagnosis observer

This paper studies the problem of fault accommodation of time‐varying delay systems using adaptive fault diagnosis observer. Based on the proposed fast adaptive fault estimation (FAFE) algorithm using only a measured output, a delay‐dependent criteria is first established to reduce the conservatism of the design procedure, and the FAFE algorithm can enhance the performance of fault estimation. On the basis of fault estimation, the observer‐based fault‐tolerant tracking control is then designed to guarantee tracking performance of the closed‐loop systems. Furthermore, comprehensive analysis is presented to discuss the calculation steps using linear matrix inequality technique. Finally, simulation results of a stirred tank reactor model are presented to illustrate the efficiency of the proposed techniques. Copyright © 2009 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.     

Integrated design of fault detection,isolation, and control for continuous‐time Markovian jump systems

In this paper, the problem of integrated fault detection, isolation, and control design of continuous‐time Markovian jump linear systems with uncertain transition probabilities is introduced and addressed for the first time in the literature. A single Markovian jump module designated as the integrated fault detection, isolation, and control under a mixed robust framework is considered to simultaneously achieve the desired detection, isolation, and control objectives. Conventional mixed robust approaches to the fault detection and isolation problem lead to conservative results due to the selection of identical Lyapunov matrices. Consequently, the extended linear matrix inequality methodology is utilized in this work to reduce the conservativeness of standard approaches by introducing additional matrix variables so that the coupling of Lyapunov matrices with the system matrices is eliminated. Simulation results for an application to the GE F‐404 aircraft engine system illustrate the effectiveness and capabilities of our proposed design methodologies. Comparisons with relevant work in the literature are also provided to demonstrate the advantages of our proposed solutions.     

Robust fault estimation based on learning observer for Takagi-Sugeno fuzzy systems with interval time-varying delay

This paper studies the problem of robust fault estimation for a class of Takagi-Sugeno(T-S) fuzzy systems which subject to interval time-varying delay, external disturbance, and actuator fault. The designed learning observer can achieve simultaneous estimation of system state and time-varying or constant actuator fault. Then, we construct a new Lyapunov-Krasovskii functional including the information of the lower and upper delay bounds; compared with the time-varying delay, the interval time-varying delay is the less conservative form. Furthermore, one less conservative delay-dependent condition for the existence of learning observer is given in terms of linear matrix inequalities. In addition, the results for the systems with interval time-varying delay are simplified when the delay is not concluded. Finally, simulation results of two examples are presented to show the effectiveness of the proposed method.     

Stability and stabilization in switched discrete‐time systems

In this paper, we investigate the stability and stabilization problem for discrete‐time switched systems. We consider a probabilistic case where the system is switched among different subsystems, and the probability of each subsystem being active is defined as its occurrence probability. The relationship between the developed model of the switched system and the Markovian jump system is analyzed. For a switched system with a known subsystem occurrence probabilities, we give a stochastic stability criterion in terms of a linear matrix inequality. Then, we extend the results to a more practical case where the subsystem occurrence probabilities of switching are known to be constant, but their specific values are only known with some uncertainty. A new iterative approach is employed to choose the switching law between the subsystems. For unstable switched systems, mode‐dependent state feedback and static output feedback controllers are developed to achieve the stabilization objective. Finally, several simulation examples are presented to show the efficacy of the proposed criteria and methods. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust fault estimation for Takagi-Sugeno fuzzy systems with state time-varying delay

This paper deals with the problem of H_∞ robust fault estimation for a class of Takagi-Sugeno (T-S) fuzzy systems with state time-varying delay, sensor, and actuator faults. The faults considered in this paper are time-varying signals whose k-order derivatives with respect to time are bounded. Then, we propose a proportional multiple integral observer to achieve simultaneous estimation of system states and time-varying actuator and sensor faults. Furthermore, one less conservative delay-dependent sufficient condition for the existence of fault estimation observer is given in terms of linear matrix inequality. The disturbance attenuation is constrained to a given level using H_∞ performance index. Finally, simulation results of one numerical example is presented to show the effectiveness of the proposed method.     

A finite frequency approach to filter design for uncertain discrete‐time systems

This paper studies the problem of finite frequency filter design for linear time‐invariant discrete‐time systems with polytopic uncertainties. Generalized Kalman–Yakubovich–Popov lemma is exploited to formulate the filter design problem in finite frequency domain. A design method is presented in terms of solutions to a set of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed method. Copyright © 2007 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.     

Data‐driven tuning of linear parameter‐varying precompensators

Methods for direct data‐driven tuning of the parameters of precompensators for linear parameter‐varying (LPV) systems are developed. Since the commutativity property is not always satisfied for LPV systems, previously proposed methods for LTI systems that use this property cannot be directly adapted. When the ideal precompensator giving perfect mean tracking exists in the proposed precompensator parameterization, the LPV transfer operators do commute and an algorithm using only two experiments on the real system is proposed. It is shown that this algorithm gives consistent estimates of the ideal parameters despite the presence of stochastic disturbances. For the more general case, when the ideal precompensator does not belong to the set of parameterized precompensators, another technique is developed. This technique requires a number of experiments equal to twice the number of precompensator parameters and it is shown that the calculated parameters minimize the mean‐squared tracking error. The theoretical results are demonstrated in simulation. Copyright © 2009 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.     

一类不确定线性离散系统有限时间观测器设计

针对一类不确定线性离散系统有限时间观测器最优设计问题,利用线性矩阵不等式方法以及有限时间有界的概念,给出了具有不确定外部扰动输入的线性离散系统有限时间有界的充分条件.对具有状态反馈和输出的线性不确定离散系统引入有限时间观测器的概念,可以保证在给定的有限时间区间内,观测误差小于一个给定的界,并给出了最优有限时间观测器的具体设计方案.此方案的有效性可以通过仿真实验得到验证.     

Actuator fault estimation based on generalized learning observer for quasi-linear parameter varying systems

This article presents a generalized learning observer (GLO) design for the simultaneous estimation of states and actuator faults for polytopic quasi-linear parameter varying systems. The proposed approach is based on the use of a GLO, which generalized the existing results on the proportional-integral observers. Conditions of existence and stability of the observer are given through the stability analysis in the sense of Lyapunov. Its design is obtained in terms of a set of linear matrix inequalities. The performance of the proposed method is evaluated by simulation in a one-link-flexible joint robot system.     

Adaptive observer for a class of nonlinear systems with time‐varying delays

The adaptive observer design problems have been extensively studied in literature for both linear and nonlinear systems. Some researches have also been carried out on adaptive observer design for linear time‐delay systems, but there is no significant work on adaptive observer design for nonlinear time‐delay systems. In this work, the adaptive observer design problem for a class of nonlinear time‐delay systems is considered. The observer is designed for the nonlinear systems whose nonlinear functions satisfy Lipschitz condition. Like conventional adaptive observers for the systems without time delays, this observer also estimates both states and unknown parameters simultaneously. For this property, it will be very much useful for many real‐time systems where time delays cannot be avoided. The sufficient conditions for existence of the observer are derived using the linear matrix inequality approach. With the help of a numerical example, effectiveness of the proposed observer is demonstrated. Copyright © 2012 John Wiley & Sons, Ltd.     

Fault estimation and tolerant control for discrete‐time switched systems with sojourn probabilities

This paper addresses the issue of fault estimation and accommodation for a discrete‐time switched system with actuator faults. Here, we assume that the sojourn probabilities are known a priori. By using the reduced‐order observer method, the sojourn probability approach, and the Lyapunov technique, a fault estimation algorithm is obtained for the considered system. The main objective of this work is to design a dynamic output feedback fault‐tolerant controller based on the obtained fault estimation information such that the closed‐loop discrete‐time switched system with available sojourn probabilities is robustly mean‐square stable and satisfies a prescribed mixed and passivity disturbance attenuation level in the presence of actuator faults. More precisely, a dynamic output feedback fault‐tolerant controller is established in terms of linear matrix inequalities. Finally, numerical examples are provided to illustrate the usefulness and effectiveness of the proposed design technique.     

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.     

Threshold computation for fault detection in linear discrete‐time Markov jump systems

This paper proposes a threshold computation scheme for an observer‐based fault detection (FD) in linear discrete‐time Markovian jump systems. An observer‐based FD scheme typically consists of two stages known as residual generation and residual evaluation. Even information of faults is contained inside a residual signal, a decision of faults occurrence is consequently made by a residual evaluation stage, which consists of residual evaluation function and threshold setting. For this reason, a successful FD strongly depends on a threshold setting for a given residual evaluation function. In this paper, Kalman filter (KF) is used as a residual generator. Based on an accessibility of Markov chain to KF, two types of residual generations are considered, namely mode‐dependent and mode‐independent residual generation. After that threshold is computed in a residual evaluation stage such that a maximum fault detection rate is achieved, for a given false alarm rate. Without any knowledge of a probability density function of residual signal before and after fault occurrence, a threshold is computed by using an estimation of residual evaluation function variance in a fault‐free case. Finally, a detection performance is demonstrated by a numerical example. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive iterative learning control of discrete‐time varying systems with unknown control direction

Without using Nussbaum gain, a novel method is presented to solve the unknown control direction problem for discrete‐time systems. The underlying idea is to fully exploit the convergence property of parameter estimates in well‐known adaptive algorithms. By incorporating two modifications into the control and the parameter update laws, respectively, we present an adaptive iterative learning control scheme for discrete‐time varying systems without the prior knowledge of the sign of control gain. It is shown that the proposed adaptive iterative learning control can achieve perfect tracking over the finite time interval while all the closed‐loop signals remain bounded. An illustrative example is presented to verify effectiveness of the proposed scheme. Copyright © 2012 John Wiley & Sons, Ltd.