Stabilization Design Of A Class Of Switched Systems With State Constraints

Switched systems and nonlinear systems have attracted much attention because of their important theoretical research significance and extensive practical applications.The study of switched systems and nonlinear systems is helpful to improve the stability and control accuracy of the systems,and also promotes the development of control theory.In recent years,the research of nonlinear systems and switched systems has made great progress,and a lot of valuable research results have been obtained.However,in practical application,many systems are affected by security specifications or hardware conditions during operation and there are state constraints.Violating these state constraints may result in performance degradation or even security problems.Therefore,the control prob-lem of systems with state constraints has become one of the frontier research problems in the control field.Starting from state constraints,this paper will study switched systems and nonlinear systems respectively.The main research contents are as follows:In Chapter 1,we present a survey.Firstly,a brief overview of switched systems and nonlinear systems are given.Then,the prescribed-time stability and state constraint are introduced respectively.In Chapter 2,the stability analysis of switched systems with state constraints under pre-specified dwell time switching signals is studied.The state of the switched systems is constrained to a unit hypercube.Firstly,the saturation function is used to transform the state constraints into a saturation problem,and the saturation problem is transformed into a convex hull technique to deal with the state constraints according to the definition of set coverage.Secondly,a class of multiple time-varying Lyapunov functions is constructed,and the sufficient condition for the stability of the switched systems are given under the framework of pre-specified dwell time switching.Furthermore,the constructed Lyapunov functions contain two time-varying functions,one of which contains the jump rate.This introduces a certain degree of freedom into the design of dwell time switching signals.Such Lyapunov functions can reduce energy at switching time and eliminate the“jump”phenomena of adjacent Lyapunov functions at switching time.Subsequently,an iterative linear matrix inequality algorithm is proposed to verify the sufficient condition.Finally,two examples are given to show the effectiveness of the method.In Chapter 3,the stabilization of state-constrained switched systems with all unsta-ble subsystems is studied.The state of the switched systems is constrained to a unit hypercube.Firstly,the saturation technique is used to deal with state constraints,and then the saturation problem is transformed into convex hull technique.Secondly,a class of multiple time-varying Lyapunov functions is constructed,which limits the dwell time by a pair of upper and lower bounds,constrains the growth of the Lyapunov function,and limits the energy decline of the switched systems at switching time.Based on the dwell time switching technique,the sufficient condition for globally uniform asymptotic stabilization of state-constrained switched systems with all unstable subsystems are given.Finally,two examples demonstrate the effectiveness of the proposed method.In Chapter 4,the prescribed-time stabilization of nonlinear systems with state con-straints is studied.The settling time of the nonlinear systems can be prescribed by the designer,independent of parameters and initial conditions.Firstly,the barrier Lyapunov function is used and a time-varying coordinate transformation is carried out.Secondly,a new stabilization function is constructed by adding a time term and using an improved L_gV-backstepping method.Such stabilization function can make the state of the non-linear systems converge to zero in any desired settling time without violating the state constraint,and then keep at zero,which means that the nonlinear systems can still run uninterrupted after the settling time.In addition,the designed controller can be regarded as a switching controller composed of two sub-controllers,which can achieve control ob-jectives without violating state constraints.Finally,an example is given to demonstrate the effectiveness of the proposed method.In Chapter 5,the main research content of this paper is summarized,and the direction of future research is indicated.