Direct model reference adaptive control using Kp = LDU factorization for multivariable discrete-time plants

For a large class of discrete-time multivariable plants with arbitrary relative degrees, the design and analysis of the direct model reference adaptive control scheme are investigated under less restrictive assumptions. The algorithm is based on a new parametrization derived from the high frequency gain matrix factorization Kp=LDU under the condition that the signs of the leading principal minors of/fp are known. By reproving the discrete-time Lp and L2σ norm relationship between inputs and outputs, establishing the properties of discrete-time adaptive law, defining the normalizing signal, and relating the signal with all signals in the closed-loop system, the stability and convergence of the discrete-time multivariable model reference adaptive control scheme are analyzed rigorously in a systematic fashion as in the continuous-time case.     

Robust fault detection filter design for uncertain LTI systems based on new bounded real lemma

This paper concerns the problem of robust fault detection filter design for uncertain linear time-invariant (LTI) systems with both model uncertainty and disturbances. Firstly, the fault detection filter design is formulated to H _∞ model-matching problem. Secondly, based on a new bounded real lemma, a sufficient condition for the existence of the robust fault detection filter is constructed in term of linear matrix inequalities (LMIs). Owing on the introduction of the tuning parameter and slack variables in obtained LMI condition, the proposed design method can provide higher fault detection sensitivity performance than the existing one. Finally, an illustrative example is employed to demonstrate the effectiveness of the proposed approach. Recommended by Editorial Board member Bin Jiang under the direction of Editor Jae Weon Choi. This work was supported by Postdoctoral Fundation of Jiangsu Province under grant 0901026c and Key Laboratory of Education Ministry for Image Processing and Intelligent Control under grant 200805. Tao Li received the Ph.D. degree in the Research Institute of Automation Southeast University, China. Now He is a postdoctoral researcher with the same university. His current research interests include time-delay systems, neural networks, robust control, fault detection and diagnosis. Lingyao Wu received the Ph.D. degree in the Research Institute of Automation Southeast University, China. Now He is an Assistant Professor in the Research Institute of Automation Southeast University. His current research interests include time-delay systems, neural networks, robust control, fault detection and diagnosis. Xinjiang Wei was born in Dongying, China, in 1977. He received the B.S. degrees from Yantai Normal University, China in 1999, M.S. degrees from Bohai University in 2002, and the Ph.D. degree in Department of Information from Northeastern University in 2005. From 2006 to Present, he was with Ludong University as an Associate Professor. From 2006 to 2009, he was a Postdoctoral Fellow at Southeast University. His research interests include robust control, nonlinear control, and fuzzy control.     

局部引理及其在（r，s）-SAT问题中的应用

一般说来,寻找满足一定结构性质的对象结构是困难的。概率方法提供了解决此类问题的途径：证明满足一定结构性质的对象的概率大于零。在概率方法中,局部引理是一个关键技术。本文介绍了局部引理的基本原理和使用方法,并将其应用到估计（r,s）-SAT问题中临界函数的下界。     

Infinite Markov jump-bounded real lemma

A bounded real lemma is established, providing an equivalent condition to stochastic stability (SS) of a continuous-time infinite Markovian jump linear system (MJLS) with a prescribed L₂-stochastic disturbance attenuation level γ in terms of existence of solutions to an infinite set of coupled linear matrix inequalities (LMIs). Besides the interest in its own right, the main result provides a fundamental tool for the development of an H_∞-like theory devoted to this class of systems.     

A general method for function synthesis†

This paper proposes some mathematical relations that may be used to describe conditions in systems after connections have been altered. The common rules of conservation of charge and flux emerge as particular instances of these more general relations. The results obtained apply in systems containing amplifiers (subject to model adequacy)—a case excluded by the normal conservation stipulations.

The conditions under which a peculiar form of instability is encountered are presented.     

Control synthesis via state feedback with finite frequency specifications for time-delay systems

This article considers the problem of control synthesis via state feedback for linear time-delay systems with design specifications in finite frequency ranges. First, a finite frequency performance analysis condition for time-delay systems is presented. Then, a resulting state feedback control synthesis condition is given in terms of solutions to a set of linear matrix inequalities (LMIs). Finally, the design procedure and the effectiveness of the proposed method are illustrated via a numerical design example.     

Active fault tolerant control for a class of linear time-delay systems in finite frequency domain

This article deals with the problem of active fault tolerant control (AFTC) for a class of linear time-delay systems in a finite frequency domain. A new ?_∞ controller in generalised internal model control architecture with an observer-based fault estimator is proposed for the AFTC system. Based on online fault estimation and accommodation, the closed-loop system stability and ?_∞ performance for both fault free and faulty cases are guaranteed. With the aid of the generalised Kalman–Yakubovich–Popov lemma for time-delay systems, sufficient conditions on the existence of such an AFTC system ensuring simultaneous finite frequency estimation and control performance are derived. The calculation procedure of the parameter matrices of the fault estimator and ?_∞ controller is also proposed. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.     

Indirect adaptive fuzzy and impulsive control of nonlinear systems

The problem of indirect adaptive fuzzy and impulsive control for a class of nonlinear systems is investigated. Based on the approximation capability of fuzzy systems, a novel adaptive fuzzy and impulsive control strategy with supervisory controller is developed. With the help of a supervisory controller, global stability of the resulting closed-loop system is established in the sense that all signals involved are uniformly bounded. Furthermore, the adaptive compensation term of the upper bound function of the sum of residual and approximation error is adopted to reduce the effects of modeling error. By the generalized Barbalat's lemma, the tracking error between the output of the system and the reference signal is proved to be convergent to zero asymptotically. Simulation results illustrate the effectiveness of the proposed approach.     

General-demand disjoint path covers in a graph with faulty elements

A k-disjoint path cover of a graph is a set of k internally vertex-disjoint paths which cover the vertex set with k paths and each of which runs between a source and a sink. Given that each source and sink v is associated with an integer-valued demand d(v)≥1, we are concerned with general-demand k-disjoint path cover in which every source and sink v is contained in the d(v) paths. In this paper, we present a reduction of a general-demand disjoint path cover problem to an unpaired many-to-many disjoint path cover problem, and obtain some results on disjoint path covers of restricted HL-graphs and proper interval graphs with faulty vertices and/or edges.     

Farkas引理及其应用

由凸集分离定理引出了Farkas引理,进而给出了3个择一性定理,并运用Farkas引理和择一性定理,证明了优化中的KT定理、可行域算法中的KT条件、广义优化中的Tucker引理和博弈论中的Minmax定理.