Linear Quadratic Optimal Control for Systems Governed by First-Order Hyperbolic Partial Differential Equations  

作　　者：XUE Xiaomin XU Juanjuan ZHANG Huanshui 

机构地区：[1]School of Control Science and Engineering,Shandong University,Jinan 250061,China [2]College of Electrical Engineering and Automation,Shandong University of Science and Technology,Qingdao 266000,China

出　　处：《Journal of Systems Science & Complexity》2024年第1期230-252,共23页系统科学与复杂性学报（英文版）

基　　金：supported by the National Natural Science Foundation of China under Grant Nos.61821004 and 62250056;the Natural Science Foundation of Shandong Province under Grant Nos.ZR2021ZD14 and ZR2021JQ24;Science and Technology Project of Qingdao West Coast New Area under Grant Nos.2019-32,2020-20,2020-1-4,High-level Talent Team Project of Qingdao West Coast New Area under Grant No.RCTDJC-2019-05;Key Research and Development Program of Shandong Province under Grant No.2020CXGC01208.

摘　　要：This paper focuses on linear-quadratic(LQ)optimal control for a class of systems governed by first-order hyperbolic partial differential equations(PDEs).Different from most of the previous works,an approach of discretization-then-continuousization is proposed in this paper to cope with the infinite-dimensional nature of PDE systems.The contributions of this paper consist of the following aspects:(1)The differential Riccati equations and the solvability condition of the LQ optimal control problems are obtained via the discretization-then-continuousization method.(2)A numerical calculation way of the differential Riccati equations and a practical design way of the optimal controller are proposed.Meanwhile,the relationship between the optimal costate and the optimal state is established by solving a set of forward and backward partial difference equations(FBPDEs).(3)The correctness of the method used in this paper is verified by a complementary continuous method and the comparative analysis with the existing operator results is presented.It is shown that the proposed results not only contain the classic results of the standard LQ control problem of systems governed by ordinary differential equations as a special case,but also support the existing operator results and give a more convenient form of computation.

关 键 词：Discretization-then-continuousization method first-order hyperbolic partial differential equations forward and backward partial difference equations linear quadratic optimal control. 

分 类 号：O232[理学—运筹学与控制论]