1. Linear Quadratic Optimal Control for Systems Governed by First-Order Hyperbolic Partial Differential Equations.
- Author
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Xue, Xiaomin, Xu, Juanjuan, and Zhang, Huanshui
- Abstract
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. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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