Robust Stabilization And Tracking Control For Switched Systems With Constrained Input And State

Switched syetems have received more attention from many reseachers,due to the needs of the practical application and theoretical development.The dynamic of switched systems is not the superposition of the dynamic of each subsystem,and it is extremely rich.Thus,the study of switched systems is more complicate than that of general nonswitched systems.A dynamical system is called a positive system if its state is always confined in the nonnegative orthant for any nonnegative initial condition.For a switched system,if the state always keeps nonnegative for any nonnegative initial condition under arbitrary switching signal,then this system is called a switched positive system.In fact,switched positive systems are able to describe a class of practical switched systems whose state always keeps nonnegative more accurately.So the study on switched positive systems is of great significance.Due to the hard limit of the physical components,the actuator saturation often exists in the practical engineering control.It may degrade the performance of practical control systems,and even destroy the stability of systems.Therefore,the phenomenon of the actuator saturation can not be ignored.In addition,the tracking control is a classical control proplem in the control theory and control engineering,while the results on the tracking control of switched positive systems are quite few.The main reason is that the problem itself is complicated and difficult to deal with.For two classes of switched systems with constrained input and state,this dissertation investigates the problems of stabilization and tracking control.The main contributions are as follows.(1)We study the stabilization of a class of cascade switched nonlinear systems with actuator saturation.Each subsystem of such switched systems is comprised of a linear part and a nonlinear part,and the linear part consists of stablizable subsections and unstablizable subsections.For each subsystem,we design the state feedback controller.Using the convex hull technique and the extended dwell time method,we present the sufficient conditions in terms of LMIs for the solvability of the exponential stabilization of the closed-loop system.(2)Adopting the piecewise Lyapunov function method and the convex hull technique,we investigate the robust stabilization and weighted L2-gain performance analysis for a class of switched systems with actuator saturation.First,we propose sufficient conditions in terms of LMIs for the solvability of the robust stabilization for switched systems without disturbance.Second,with a class of disturbances whose energies are bounded by a given constant,we also derive the conditions that the closed-loop system has weighted L2-gain performance under the dwell time scheme.At last,we give the largest disturbance tolerance through solving a constrained optimization problem.(3)For a calss of switched systems with actuator saturation,we improve the transient performance of output tracking control via the composite nonlinear feedback control technique.First,a design procedure of constructing the composite nonlinear feedback control law is presented.Under the average dwell time scheme,the controlled output of the closed-loop system tracks asymptotically a step reference signal by the composite nonlinear feedback control technique,without exceeding the saturation limit.At the same time,the desired transient performance with quick response and small overshoot can be achieved.In addition,when the tracking control problem of each subsystem is unsolvable,we present another method which is the composite nonlinear feedback control technique in the state-dependent switching law.We conduct the dual designs of the composite nonlinear feedback controller and the switching law.(4)Through multiple linear co-positive Lyapunov functions and the convex hull technique,we study the stabilization of switched positive systems with actuator saturation.First,for the time-dependent switching case,we design a state feedback controller such that the closed-loop system is exponential stability.Second,for the state-dependent switching case,we conduct the dual designs of the switching signal and the controller.This method is applicable to the case that each subsystem is unstable.Third,the proposed method is extended to switched positive systems with time delay subject to actuator saturation.(5)We concentrates on the output tracking control problem with L1-gain performance of switched positive systems via adopting the multiple co-positive Lyapunov functions technique.The proposed approach is still effective even though the output tracking control problem of any subsystem is unsolvable.First,when the state is available,we conduct the dual designs of the state feedback controller and the state dependent switching signal.Second,when the state is not available,we design the output feedback controller and the error-dependent switching signal.(6)We investigate the tracking control without overshoot for switched positive systems.The state unilateral tracking guarantees the whole course of tracking without overshoot.Via the dual designs of both the controller and the switching signal,the state unilateral tracking control problem with L1-gain performance for switched positive systems is solved through adopting multiple linear co-positive Lyapunov functions technique.In terms of different assumptions,two techniques are presented in order to deal with the state unilateral tracking problem.Moreover,the design method is applicable to the case that the unilateral tracking control problem is unsolvable for any subsystem.The conclusions and perspectives are provided in the end of this dissertation.