Memory Output Feedback Control and Filtering for Dynamical Systems in Finite Frequency Domain

有限頻域內動態系統的有記憶輸出反饋控制與濾波

Student thesis: Doctoral Thesis

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Award date27 Aug 2018

Abstract

The output feedback control and filtering design problems of dynamical systems have been receiving considerable attention because in most cases, not all the system states are measurable for real-world systems. From a practical point of view, it is of great significance to develop advanced output feedback control and filtering design approaches to reduce design conservatism and achieve better performances. It is observed that traditional control and filtering design methods often do not make full use of some available information, for example past output measurements and/or frequency spectrum of disturbances, and as a consequence, the obtained results tend to be conservative. On the other hand, the advanced development in information processing capacities of controllers and filters makes them possible to store and use additional past output measurements for reduction of design conservatism. In addition, in most practical situations, disturbances are not in a full frequency range instead are often restricted in a finite frequency range. Therefore, memory output feedback control and filtering for dynamical systems in finite frequency domain is a research subject of great practical and theoretical significance, and thus deserves further investigation.

In this thesis, a number of finite frequency memory output feedback control and filtering design approaches are developed for linear systems with polytopic uncertainties and complex nonlinear systems via Takagi-Sugeno (T-S) fuzzy affine models, respectively. The main effort is devoted to the development of novel finite frequency memory control and filtering strategies for reducing design conservatism and improving performances. The merit of the proposed approaches lies in their less design conservatism and better control/filtering performances, which is realized by utilizing some extra information including the past output measurements and frequency spectrum of the disturbances. It is also shown that the proposed approaches are more general and include the traditional memoryless and full frequency control and filtering approaches as their special cases. The main results can be summarized as follows.

Firstly, we study the problem of finite frequency memory fixed-order output feedback controller design for polytopic uncertain linear systems in finite frequency domain. Via the system state-input augmentation, a novel descriptor system approach is developed to facilitate controller synthesis, which transforms the resulting closed-loop system into a corresponding descriptor system. A sufficient condition for the regularity, causality, and asymptotic stability with finite frequency H-infinity performance is obtained for the resulting closed-loop descriptor system. The corresponding finite frequency memory dynamic output feedback control law together with optimal finite frequency H-infinity performance index are presented by solving a set of linear matrix inequalities (LMIs). Moreover, by choosing different design parameters, the memory static output feedback controller, the memoryless dynamic output feedback controller, and the memoryless static output feedback controller design results can also be obtained as special cases. It is theoretically proven that the H-infinity performance can be enhanced by the utilization of memory output feedback control strategy.

Secondly, attention is focused on the problem of memory filtering design for polytopic uncertain linear systems in finite frequency domain. Based on additional past output measurements together with parameter-dependent Lyapunov functions and Parseval's theorem, a new sufficient condition for robust asymptotic stability with finite frequency H-infinity performance is obtained for the filtering error system. The corresponding filter gains together with optimal finite frequency H-infinity performance index can be obtained by solving a set of LMIs, which can be solved efficiently by using optimization techniques. The advantages of the proposed finite frequency memory filtering strategy for polytopic uncertain discrete-time systems is validated by both theoretical analysis and simulation examples.

Then, attention is focused on the problem of piecewise affine memory output feedback control for nonlinear systems in finite frequency domain, where the nonlinear systems are represented by norm-bounded uncertain T-S fuzzy affine systems. In order to use piecewise fuzzy Lyapunov function based approach to reduce design conservatism, the premise variable space of T-S fuzzy affine systems is decomposed into two kinds of subspaces, i.e., the crisp subspaces and fuzzy subspaces. Based on piecewise fuzzy Lyapunov functions and a novel linearization technique, the approach to the design of robust finite/full frequency, piecewise affine/linear, memory/memoryless and dynamic/static output feedback controllers is proposed in a unified framework by solving a set of LMIs. With the obtained controller, the closed-loop system is robust asymptotically stable with a prescribed finite frequency H-infinity performance.

Finally, we study the problem of piecewise affine memory filtering design for norm-bounded uncertain T-S fuzzy affine systems in finite frequency domain. Based on piecewise fuzzy Lyapunov functions, S-procedure and Projection lemma, the admissible robust finite/full frequency, memory/memoryless, piecewise affine/linear filter synthesis is carried out in a unified framework, which guarantees that the resulting filtering error system is asymptotically stable with a given finite frequency H-infinity performance. Moreover, by choosing different design parameters, the piecewise affine memory filter design results can reduce to piecewise linear and/or memoryless filters design results.

    Research areas

  • Memory control and filtering, Finite frequency H-infinity performance, Polytopic uncertain linear systems, Takagi-Sugeno fuzzy systems