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State Estimation and Indefinite Linear Quadratic Control for Generalized Systems

Author: CuiPeng
Tutor: ZhangChengHui;ZhangHuanShui
School: Shandong University
Course: Control Theory and Control Engineering
Keywords: Generalized Linear Systems Optimal State Estimation State Observer Linear Indefinite Quadratic Optimal Control
Type: PhD thesis
Year: 2008
Downloads: 183
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Two essential problems, including linear optimal state estimation and linear quadratic optimal control, of linear generalized systems are researched. Compared with standard state-space model, generalized systems are more general description of dynamic systems. Generalized systems are important because this model in many situations allows one to use all the physical information available and consequently generalized system models give more insight, convenience and generality for applications than traditional state-space models do. However, most of theories and methods dealing with regular systems (standard state-space models) are not directly applied for the characters of generalized systems, then new theories and techniques need to be developed.Linear optimal state estimation is always one of the essential question of control theoretics and applications. It is mainly Kalman filtering for stochastic systems and observer design for determinate systems. Additionally, linear quadratic optimal control, which is also called linear quadratic regulation, is also one of the essential question of control theoretics. Some hot topics like H_Ôł×filtering can be researched in virtue of discussion of linear quadratic optimal control of dual systems. It is worth pointed out that indefinite linear quadratic optimal control problem, which has attracted much more attention in recent years, not only extends the theory of linear quadratic optimal control, but also helps to solve many problems occurred in finance and biology fields. Then, the two classes of problem have always been active research areas though there are many literatures to discuss them.Some new techniques and methods like Krein Space will be applied and some classical theories like Riccati equation and Linear Matrix Inequality(LMI) will be deeply discussed when the two problems for generalized systems are researched. Consequently, some results are improved or new problems are presented. This thesis mainly includes the following three aspects:1. A new estimate arithmetic is presented for linear optimal state estimation of generalized systems. The assumption is only regularity of generalized systems. The filter is derived by solving two coupled Riccati-type difference equations. The approach is based on projection formula in Hilbert space.2. Observer design of generalized linear systems with state time-delay and unknown inputs is researched. The corresponding design steps and observer-based feedback stabilizing controller are presented by using linear matrix inequality.3. Linear quadratic optimal control problem for generalized linear systems and ones with multiple input delays is extended to indefinite LQ problem. Necessary and sufficient conditions guaranteeing existence of unique solution of the indefinite LQ problem are given by using Krein space. Meanwhile, optimal controller whose dimensions are same as those of the original systems is obtained.Innovations of the thesis mainly include the following three aspects:For filtering of regular generalized systems, the technique only used is projection theorem in Hilbert space and the method is to solve two coupled Riccati-type difference equations;For generalized linear systems with state time-delay and unknown inputs, the algorithms of state observe design and observer-based feedback stabilizing controller design are presented by using matrix theory and linear matrix inequality.For indefinite linear quadratic optimal control problem of determinate generalized system, necessary and sufficient conditions guaranteeing existence of unique solution and an explicit solution of optimal controller are obtained by using a kind of indefinite-metric space-Krein space. For that of generalized linear systems with multiple input delays, optimal controller whose dimensions are same as those of the original systems is obtained.

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