Robust Control For Complex Control Systems With Similarity

In many naturally evolving large-scale systems such as biological systems, socialsystems and management systems, a frequently observed fundamental feature is thatsome subsystems commonly possess similar structure. With their developments, theymust adapt themselves to circumstances and require moving optimally. Therefore,step by step, themselves form their structures through optimal evolution. This alsooccurs widely in engineering systems. How these systems are described andcontrolled? How these systems work? This is an important project of the researchesfor the complex systems. In this paper, for a class of complex control systems withsimilar structures, the problems of description and control are discussed. Thecorresponding results show that the similar structures can simplify the analysis andcontroller design. The dynamical behavior of systems with similarity depends mainlyon the information from the similar structure and certain special subsystem.The paper may be summarized as follows:In the first chapter, the main background considered in this paper is introduced.Then, the control systems with similarity are mathematically described in detail.Meanwhile, many practical examples are given to illustrate the conception of similarcontrol systems and the wide existence in engineering systems. In the second chapter, the state feedback control for a class of complex controlsystems with similarity is considered. Under the conditions that the uncertaintiessatisfy the matched condition and unmatched condition, the robust controller isdesigned, respectively, through which, the role that the similar structure plays insystem analysis and design is showed. Meanwhile, in this chapter, some algorithmsfor similar parameters are given, and the linear robust decentralized controller isdesigned.In the third chapter, output feedback control for a class of complex control systemswith similarity is considered. Generally speaking, it is difficult to design a robustoutput feedback controller because only partial information can be available.However, through the discussion in this chapter, it is noted that similar structuressimplify the robust output feedback design.In the chapter 4, the state observer synthesis for a class of complex control systemswith similarity is considered. It is showed that the state observer design is simplifiedby using the information from similar structures. Meanwhile, the adaptive stateobserver is also considered in this chapter. The corresponding results show that thesimilar structure can simplify the adaptive mechanism.In the chapter 5, the robust output tracking between two similar control systems isdiscussed, which is proposed on the background of aggregation in the theory oflarge-scale systems. It is showed that similar structure can simplify the trackingcontrol design and improve the tracking performance.Finally, some existed problems in the researches for complex systems withsimilarity are explained.