Optimality recovery of feedback control system based on discrete-time state dependent riccati equation

Author

Yoshida, Kenta ; Ohsaki, Hiroyuki ; Iwase, Masami

Author_Institution

Dept. of Robot. & Mechatron., Tokyo Denki Univ., Tokyo, Japan

fYear

2012

fDate

3-5 Oct. 2012

Firstpage

463

Lastpage

469

Abstract

In this paper, optimality recovery of a control method based on the discrete-time state-dependent Riccati equation (DSDRE) is discussed. The relationship between the DSDRE method and the Hamilton-Jacobi-Bellman equation (HJBE) concerned with optimal control for discrete-time nonlinear systems is addressed briefly. Based on the relationship, the stability of the DSDRE method is investigated with the Lyapunov theorem. As a result, the asymptotical stability holds for the DSDRE strategy is proven for some special case, and the optimality does not hold under infinite-horizon criteria in general. Hence an iterative numerical method is proposed to improve and recover the optimality along a state trajectory obtained by the DSDRE strategy. The method is verified through numerical simulations.

Keywords

Lyapunov methods; Riccati equations; asymptotic stability; discrete time systems; feedback; iterative methods; nonlinear control systems; optimal control; DSDRE method; Hamilton-Jacobi-Bellman equation; Lyapunov theorem; asymptotical stability; discrete time nonlinear system; discrete time state dependent Riccati equation; feedback control system; iterative numerical method; optimal control; optimality recovery; state trajectory; Indexes; Numerical stability; Optimal control; Riccati equations; Stability criteria; Trajectory;

fLanguage

English

Publisher

ieee

Conference_Titel

Control Applications (CCA), 2012 IEEE International Conference on

Conference_Location

Dubrovnik

ISSN

1085-1992

Print_ISBN

978-1-4673-4503-3

Electronic_ISBN

1085-1992

Type

conf

DOI

10.1109/CCA.2012.6402729

Filename

6402729