Dissipativity And Adaptive Control For Switched Nonlinear Systems

Switched system has been paid much attention because of its wide application background.On the other hand,dissipative theory is a powerful tool for analysis and design of nonlinear systems and has formed the theoretical system of the system.However,the research on the dissipativity of switched systems,especially uncertain switched systems,has not been completed yet.In this thesis,we mainly study the quasi-dissipativity and quasidissipativity-based adaptive stabilization and tracking of switched nonlinear systems.The effectiveness of the proposed method is verified by simulation.The main contents are summarized as follows:(1)For a class of switched discrete-time nonlinear systems,the problems of output feedback passification and adaptive stabilization are studied.First,a passivity concept is proposed for switched discrete-time nonlinear systems by using multiple storage functions and multiple supply rates.Then,sufficient conditions for such systems to be passive are obtained.Second,for a given switching signal,the output feedback passification problem for switched discrete-time nonlinear systems is solved under the condition that its zero dynamics is passive.Furthermore,adaptive stabilization is achieved by combining the output feedback passification design technique with a switched adaptive control technique.Finally,a lower bound on the ratio of total activation time between feedback passive and non-feedback passive subsystems is obtained to guarantee passive zero dynamics.(2)For the switched discrete-time nonlinear system,the geometrical quasi-dissipativity and boundedness are studied.First,a geometrical quasi-dissipativity concept is proposed.And the uniform ultimate boundedness of a geometrically quasi-dissipative nonlinear switched system is proved.Copared with conventional dissipative system,quasidissipative system can produce energy by itself.Second,a sufficient condition to be geometrically quasidissipative is given by designing a more general state-dependent switching law.Finally,a compatial switching law is designed to render the interconnected switched system geometrically quasi-(Q,S,R)dissipative.(3)For the switched discrete-time nonlinear system,almost passivity is investigated,and the boundedness property is obtained.First,an almost passivity concept is proposed.Based on the concept of almost passivity,the uniform ultimate boundedness of the switched nonlinear system is obtained.Almost passivity means that each activated subsystem is passive outside of a sphere,and is more extensive than geometric quasi-passivity.Second,the almost passivity conditions for switched discrete nonlinear systems are given.A more general switching law design than the min switching law is proposed.Finally,the feedback almost passification is achieved by the design of switching law and controllers.(4)The problems of exponential quasi-passivity and stabilization of switched nonlinear system are studied.First,a concept of exponential quasi-passivity is proposed for general switched nonlinear systems by using the multiple storage functions method.Second,the quasi-passification method is combined with backstepping technique to solve quasi-passification and practical stabilization problems for the switched strict feedback system by designing a state-dependent switching signals and state feedback controllers constructively.This result overcomes the restriction of relative order 1 and minimum phase.(5)For lower triangular switched nonlinear systems with unknown functions,adaptive tracking control is achieved by using the established exponential quasi-passivity theory.First,the exponential quasipassivity concept is proposed to describe the energy changing of the overall switched nonlinear systems without the exponential quasi-passivity property of all the subsystems.Then,for switched nonlinear systems,the semiglobally uniformly ultimate boundedness is achieved by using exponential quasipassivity.Second,this result is applied to solve adaptive tracking control problem uncertain switched nonlinear systems in lower-triangular form.The unknown nonlinear functions are approximated by the radial basis function neural networks.A new adaptive tracking control technique is developed by combining quasi-passification methods with adaptive backstepping techniques.