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

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

扫码查看
原文链接
  • NETL
  • NSTL
  • 万方数据
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.

Discretization-then-continuousization methodfirst-order hyperbolic partial differential equationsforward and backward partial difference equationslinear quadratic optimal control

XUE Xiaomin、XU Juanjuan、ZHANG Huanshui

展开 >

School of Control Science and Engineering,Shandong University,Jinan 250061,China

College of Electrical Engineering and Automation,Shandong University of Science and Technology,Qingdao 266000,China

国家自然科学基金国家自然科学基金山东省自然科学基金山东省自然科学基金Science and Technology Project of Qingdao West Coast New AreaScience and Technology Project of Qingdao West Coast New AreaScience and Technology Project of Qingdao West Coast New AreaHigh-level Talent Team Project of Qingdao West Coast New Area山东省重点研发计划

6182100462250056ZR2021ZD14ZR2021JQ242019-322020-202020-1-4RCTD-JC-2019-052020CXGC01208

2024

10.1007/s11424-024-3324-8

系统科学与复杂性学报(英文版)
中国科学院系统科学研究所

系统科学与复杂性学报(英文版)

EI
影响因子：0.181
ISSN：1009-6124
年,卷(期)：2024.37(1)
  • 40