Passive Control For Several Classes Of Nonlinear Lower Triangular Systems

Nonlinear systems have been widely applied in many various fields.The study of nonlinear systems theory has gradually become the focus in the field of control as a result of the inherent nonlinear property of objects.This paper focuses on passive control problem for several classes of high order nonlinear lower triangular systems.Firstly,we introduce the nonlinear lower triangular systems,passivity and the passive control problem for systems.The structure and contents of this paper are also briefly introduced.Then we deal with the passive control for the first power nonlinear lower triangular systems with uncertainty.The passive feedback control law of the system and its design method are obtained.We study the system with uncertainties.In each iteration of the back-stepping method,an observer is added to eliminate the uncertainties.The conditions which the observer has to be satisfied are given.The design method of passive controller are obtained.Next,the passive control problem for a class of nonlinear systems with odd integer powers is studied,and the existence condition and design method of the feedback passive controller for such systems are obtained.By adding a power integrator the iteration design process of the feedback passive controller and the passive control law are obtained.At last,we study the passive control of polynomial nonlinear lower triangular systems.The passive controller is designed by using the idea of controlling the nonlinear term with a nonlinear term in the method of adding a power integrator.The iterative design process and final control law of feedback passive controllers for polynomial nonlinear lower triangular systems are given.The effectiveness of these design methods are illustrated by some examples.