Discounted-cost Linear Quadratic Regulation Of A Class Of Switched Linear Systems

As a particular class of hybrid systems,switched systems are of great significance in both theoretical value and engineering applications.Switched systems have a wide range of practical engineering application,such as aerospace field,chemical,biology,economics,and so on.On the other hand,the linear quadratic optimal control is one of the most important optimization synthesis problems in switched linear system.The stabilization of an equilibrium point via optimal control techniques has long been used as a method for computing feedback stabilizers,particularly in the context of the infinite-horizon linear quadratic regulator problem.Some valuable investigates have been achieved,but many problems have not been solved.Therefore,this thesis mainly studies the linear quadratic regulator of switched systems.The main contributions are as follows:In Chapter 1,firstly,the concepts and research methods of switched systems and linear switched systems are summarized.Secondly,the research status of linear quadratic optimal control is given,and the linear quadratic optimal control of switched systems is discussed.Finally,the main content and structure of this paper are briefly introduced.In Chapter 2,we study the discounted-cost linear quadratic state regulation of a class of switched linear systems.The distinguishing feature of the proposed method is that the designed discounted-cost linear quadratic regulator will achieve not only the desired optimization index,but also the exponentially convergent of the state trajectory of the closed-loop switched linear systems.First,we adopt the embedding transformation to transform the studied problem into a quadratic-programming problem,the bang-bangtype solution of the embedded optimal control problem on a finite time horizon is the optimal solution to the original problems.Then,the computable sufficient conditions on discounted-cost linear quadratic regulator are proposed for finite-time and infinite-time horizon case,respectively.Finally,an example is provided to demonstrate the effectiveness of the proposed method.In Chapter 3,we study the discounted-cost linear quadratic output regulation of a class of switched linear systems.The distinguishing feature of the proposed method is that the designed discounted-cost linear quadratic output regulator will achieve not only the desired optimization index,but also the exponentially convergent of the output of the closed-loop switched systems.The embedding transformation technique is used to transform the studied problem of switched system into a traditional optimal control problem.Then,it is shown the bang-bang-type solution of the embedded optimal control problem is the the optimal solution to the original problems for both the finite horizon and infinite-horizon.Both the switching signal and the controller for each subsystem are designed simultaneously.Finally,an example is presented to illustrate the correctness and effectiveness of the proposed result.The main content of this paper is summarized.