Passive Control For Several Classes Of Lower Triangular Systems Based On Backstepping Technique

Nonlinear systems are widely studied and applied in various fields.Due to the complexity and diversity of nonlinear functions,it is difficult to find an effective and unified method to deal with nonlinear systems.In recent years,scholars have proposed a variety of methods and achieved considerable results.Most of these results focus on the related nature of the solution of the system and the study of stabilization problems,and the results of passive and dissipative studies on nonlinear systems from the energy point of view are relatively few.Passive control is a control method that starts from the energy angle of the system and makes the closed-loop system meet the passivity.Its physical meaning is intuitive and widely used in various practical physical systems,therefore it has attracted the attention of scholars and engineers.This paper discusses passive control problems of several classes of lower triangle systems.Firstly,we give an overview of passive control,introduce the development and research significance of passive control theory,and briefly describes the lower triangular system;The structural arrangement of this paper is pointed out,and the preliminary knowledge required for this paper is given.Then,we mainly study the passive control problem of a class of lower triangular systems.By constructing an appropriate energy function,using the sufficient conditions of passive and backstepping,we design passive feedback control law.Finally,the passive control problem for another class of lower triangular systems with uncertainties is studied.The passive feedback control law is obtained by the softer control design method,and the closed-loop system is passive.