Robust holographic control of complex interconnected systems with similar structure

With development of scientific technology, the scale of engineering systems becomes more and more large. It is required that people must deal with some complicated systems and finish complicated tasks under complicated surroundings. Therefore, we must face complicated systems seriously. In recent years, some new research methods such as modern geometric method and differential algebra method have been applied to the study of control theory according to the development of nonlinear science, and it is possible for us to solve complicated engineering systems with the development of computer science, which promotes the investigation of complicated control systems. Now, We must recognize clearly that investigation of complicated systems will be a long-term and arduous task, and it is not possible to find a valid method to deal with general complicated control systems in recent decades. But we think that to study some complicated systems with special structure at first, then, to study general complicated control systems may be a kind of valid method. In this thesis, based on the thoughts above, a class of complicated nonlinear control systems with similar structure is considered, and problems of structural holographic control and robust control are studied It is shown that both the theoretic analyzes and systems engineering design are able to be simplified by using similar structure of systems, and holographic property is closely connected with similar structure.

The thesis is summarized as follows:

In the first chapter, fundamental characteristics of general complicated systems are introduced and similar structure of complicated control systems is described. Then, some practical examples are given to illustrate the wide existences of similar systems. Finally, controllers with holographic structure are presented.

In the second chapter, state feedback centralized controllers with holographic structure are designed for some similar systems such as nonlinear time-varying composite systems, nonlinear uncertain composite systems with isolated subsystems which are single input linear systems or input-state decoupling systems, and parametric matched uncertain composite systems with isolated systems possessing uniform relative degrees. Then, state feedback decentralized controllers with holographic structure are designed for nonlinear similar large-scale systems with unmatched uncertainties. Because the controllers designed in this chapter are similar to "Bang-Bang" control and of holographic structure, it is easy to be designed in practical engineering systems.

In the third chapter, observer design of similar systems is considered. First, a kind of robust variable-structure observer is proposed for "matched" uncertain composite systems. Then, an asymptotic observer is designed for composite systems with the isolated subsystems possessing general nonlinear systems by using modern differential geometric method. It is shown that observer design can be simplified by using similar structure of systems.

In chapter 4, observer-based stabilization for nonlinear similar composite systems is discussed. The obtained results are applied to disc-shift systems. Simulation shows that the results are effective.

In chapter 5, output feedback controllers with holographic structure for nonlinear composite systems are given to be used to stabilize the systems. The advantages of this chapter are that uncertainties involved in the chapter are unmatched, and the controllers are not only decentralized but also holographic. So it's of great practical value

In chapter 6, some tracking problems are considered. A kind of iterative learning control problem is studied for a class of nonlinear similar composite systems in section 1, and robust variable structure controller is proposed for a class of similar large scale systems with matched uncertainties to track desired output in section 2.

Some problems to be investigated later and good prospects of the study of similar systems are proposed to conclude the Thesis.