Passivation Control Of Nonlinear Systems

Dissipative systems theory has been proposed since 1970 s. It plays an important role in the study of system stability. Its essential content is being a nonnegative energy function, which makes the energy consumption of the system, is less than the energy provision. We consider passivity of system, a special class of dissipative systems, in which supply rate is represented by the product of the system input and output. Passivity and feedback equivalence of nonlinear systems has occupied a central role in the nonlinear systems literature for at least three decades. And in terms of a state feedback or output feedback, Lyapunov recursive function we are able to solve, under mild regularity assumptions, the problem of identifying those nonlinear systems which are feedback equivalent to passive systems. So the key problem is to design Lyapunov recursive function and search a state feedback to passive systems.In this thesis, we solve the problem of feedback equivalence to a passive system under some mild regularity hypotheses, which can be relaxed in certain circumstances. Firstly, we introduce some fundamental work of passivity and derive a necessary and sufficient condition for the nonlinear system with the disturbance uncertainty. The result obtained can be interpreted as a robust form of the nonlinear Kalman-Yacubovich-Popov Lemma (KYP). In addition, we explain the design of Lyapunov recursive function and the basic theory of the feedback equivalence passive systems in detail.Next, we study some different models of nonlinear system separately. In the third chapter, we discuss the passivation control problem for a class of nonlinear systems with disturbance uncertainty. Passivation control problem is discussed under Hamilton Jacobi Issacs(HJI) inequality and matching conditions, respectively. Under matching conditions, the nonlinear system becomes standard form via coordinate transform; under propriety assumptions, a state feedback controller is presented to passive the closed-loop system using Lyapunov recursive design technique. In the fourth chapter, we discuss the passivation control problem for a class of nonlinear system with disturbance uncertainty and feedthrough term. We derive sufficient condition for a class of special cascade system which is obtained through the KYP lemma. The result is generalized with the help of the recursive feedback passification design technique. Inthe fifth chapter, we consider a class of nonlinear system with parametric uncertainties which is minimum phase and the parametric uncertainties are from bounded compact. Also we design a static state feedback controller, under convexity condition, to passive the closed-loop system for all admissible parametric uncertainties.In the end, we conclude this thesis and present the future work.