Online identification of time-delay jump Markov autoregressive exogenous systems with recursive expectation-maximization algorithm

This article considers the identification problem of the jump Markov autoregressive exogenous (JMARX) systems with unknown invariant time-delay under the framework of recursive expectation-maximization (REM) algorithm. In this article, a recursive Q-function is formulated for the JMARX systems, based on which the recursive sufficient statistics are obtained. Then, the parameter vectors, variance, transition probability matrix, and time-delay are recursively estimated. A numerical example and a simulated continuous fermentation reactor process are employed to illustrate the effectiveness of the proposed algorithm.     

Identification of linear systems with time delay and unknown order

This paper proposes a system identification method for linear systems with time delay and unknown order. We hypothesize a number of candidate models, which have different order, because system order is unknown. In each model, we estimate the model parameters based on the maximum likelihood method by using nonlinear optimization technique. Then both local optimization technique and global search method are used because the estimated parameters may fall into a local minimum. After all candidate model's parameters are estimated, one model is selected among these models to estimate the system order by using a posteriori probability based on Bayes's theorem. Finally, the validity of the proposed method is demonstrated by numerical examples. © 2003 Wiley Periodicals, Inc. Electr Eng Jpn, 145(3): 61–68, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10166     

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.     

Gramian‐based model order reduction of parameterized time‐delay systems

Time‐delay systems (TDSs) frequently arise in circuit simulation especially in high‐frequency applications. Model order reduction (MOR) techniques can be used to facilitate the simulation of TDSs. On the other hand, many kinds of variations, such as temperature and geometric uncertainties, can have significant impact on the transient responses of TDSs. Therefore, it is important to preserve parametric dependence during the MOR procedure. This paper presents a new parameterized MOR scheme for TDSs with parameter variations. We derive parameterized reduced‐order models (ROMs) for TDSs using balanced truncation by approximating the Gramians in the multi‐dimensional space of parameters. The resulting ROMs can preserve the parametric dependence, making it efficient for repeated simulations under different parameter settings. Numerical examples are presented to verify the accuracy and efficiency of our proposed algorithm. Copyright © 2012 John Wiley & Sons, Ltd.     

Delay‐dependent filtering design for time‐delay systems with Markovian jumping parameters

Two filtering problems—H_∞ filtering and H₂ filtering—for the linear Markovian jump systems with time delay are considered in this paper. The proposed new filtering approach guarantees that the results are less conservative than that obtained by other existing approaches. Numerical example well demonstrates the proposed algorithms. Copyright © 2006 John Wiley & Sons, Ltd.     

Optimization of Markov jump linear system with controlled modes jump probabilities

The optimal control of a Markov jump linear quadratic model with controlled jump probabilities of modes is investigated. Two kinds of mode control policies, i.e., open-loop control policy and closed-loop control policy, are considered. Using the concepts of policy iteration and performance potential, the sufficient condition needed for the optimal closed-loop control policy to perform better than the optimal open-loop control policy is proposed. The condition is helpful for the design of an optimal controller. Furthermore, an efficient algorithm to construct a closed-loop control policy, which is better than the optimal open-loop control policy, is given with policy iteration. __________ Translated from Control and Decision, 2008, 23(3): 246–250 [译自:控制与决策]     

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.     

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 observer‐based control design for uncertain singular systems with time‐delay

This paper is concerned with the stability analysis and robust dynamic output feedback controller synthesis for uncertain continuous singular systems with time‐delay. First, on the basis of the Lyapunov functional method and by resorting to the delay‐partition technique, improved delay‐dependent sufficient conditions are presented to ensure the nominal unforced system to be admissible (i.e., to be regular, impulse‐free, and stable). Second, with the help of the obtained admissibility criterion, an observer‐based controller is designed by solving a set of LMIs. Finally, the validity and applicability of the proposed approach is shown by examples. Copyright © 2013 John Wiley & Sons, Ltd.     

Decentralized adaptive robust stabilization of uncertain interconnected time‐delay systems

This paper considers the problem of decentralized adaptive robust stabilization of a class of interconnected time‐delay systems with arbitrarily bounded matched but limitedly bounded unmatched uncertainties. A new class of decentralized adaptive controllers based on Lyapunov–Krasovskii functional is proposed that guarantees bounded stability of the system and ensures nonfragileness of the controller to perturbations in its nonadaptive gain factor. The existence of such controllers is formulated in the LMI framework besides being presented using the Algebraic Riccati Equations. A numerical example is considered to illustrate the applicability and effectiveness of the proposed controller. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust adaptive control for uncertain time‐delay systems

The problem of robust stabilization for uncertain dynamic time‐delay systems is considered. Firstly a class of time‐delay systems with uncertainties bounded by high‐order polynomials and unknown coefficients are considered. The corresponding controller is designed by employing adaptive method. It is shown that the controller designed can render the closed‐loop system uniformly ultimately bounded stable based on Lyapunov–Krasovskii method and Lyapunov stability theory. Then the proposed adaptive idea is applied to stabilizing a class of large‐scale time‐delay systems with strong interconnections. A decentralized feedback adaptive controller is designed which guarantees the closed‐loop large‐scale systems uniformly ultimately bounded stable. Finally, numerical examples are given to show the potential of the proposed techniques. Copyright © 2005 John Wiley & Sons, Ltd.     

Adaptive filtering‐based multi‐innovation gradient algorithm for input nonlinear systems with autoregressive noise

In this paper, by means of the adaptive filtering technique and the multi‐innovation identification theory, an adaptive filtering‐based multi‐innovation stochastic gradient identification algorithm is derived for Hammerstein nonlinear systems with colored noise. The new adaptive filtering configuration consists of a noise whitening filter and a parameter estimator. The simulation results show that the proposed algorithm has higher parameter estimation accuracies and faster convergence rates than the multi‐innovation stochastic gradient algorithm for the same innovation length. As the innovation length increases, the filtering‐based multi‐innovation stochastic gradient algorithm gives smaller parameter estimation errors than the recursive least squares algorithm.     

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.     

An adaptive switching scheme for uncertain discrete time‐delay systems

In this paper, an adaptive switching control algorithm is proposed for the stabilization of uncertain discrete‐time systems with time‐varying delay. It is assumed that the time delay is unknown and time varying, nonetheless bounded with a known bound. It is supposed that the system is highly uncertain, and that a set of controllers are designed (off‐line) to stabilize the system in the whole uncertain parameter space; subsequently, a switching scheme is developed to stabilize the uncertain time‐delay system. A thorough stability analysis for the uncertain time‐delay system under the mentioned control scheme is provided. Furthermore, an upper bound on the allowable rate of change of the system parameters and delay is obtained. Simulation results are presented to show the efficacy of the proposed switching scheme. Copyright © 2008 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.     

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 adaptive estimation of nonlinear system with time‐varying parameters

The vast majority of available parameter estimation methods assume that the parameters to be estimated are constant or slowly time‐varying and mainly depend on a predictor or observer design so that a large adaptive gain must be used to achieve fast adaptation; this may result in high‐frequency oscillations when the system subjects to a large source of uncertainties or disturbances. This paper is concerned with adaptive online estimation of time‐varying parameters for two kinds of linearly parameterized nonlinear systems. By dividing the time into small intervals, the time‐varying parameters are approximated in terms of polynomials with unknown coefficients. Then a novel adaptive law design methodology is developed to estimate those constant coefficients, for which the parameter estimation error information is explicitly derived and used to drive the adaptations. To guarantee the continuity of the parameter estimation for all time, a parameter resetting scheme is introduced at the beginning of each interval. Finite‐time estimation convergence and the robustness against disturbances are all proved. Extensive simulation examples are provided to demonstrate the efficacy of the proposed algorithms for estimating time‐varying parameters. Copyright © 2014 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.     

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.