Approximations and Mesh Independence for LQR Optimal Control

Author

Burns, John A. ; Sachs, Ekkehard ; Zietsman, Lizette

Author_Institution

Interdisciplinary Center for Appl. Math., Virginia Polytech. Inst. & State Univ., Blacksburg, VA

fYear

2006

fDate

13-15 Dec. 2006

Firstpage

81

Lastpage

86

Abstract

The development of practical computational schemes for optimization and control of non-normal distributed parameter systems requires that one builds certain computational efficiencies (such as mesh independence) into the approximation scheme. We consider the issues of convergence and mesh independence for the Kleinman-Newton algorithm for solving the operator Riccati equation defined by the linear quadratic regulator (LQR) problem. We show that dual convergence and preservation of exponential stability (POES) play central roles in both convergence and mesh independence and we present numerical results to illustrate the theory

Keywords

Riccati equations; approximation theory; asymptotic stability; convergence of numerical methods; distributed parameter systems; linear quadratic control; mesh generation; Kleinman-Newton algorithm; LQR optimal control; approximations; dual convergence; exponential stability; linear quadratic regulator; mesh independence; nonnormal distributed parameter system control; nonnormal distributed parameter system optimization; operator Riccati equation; Computational efficiency; Control systems; Convergence of numerical methods; Distributed computing; Distributed control; Distributed parameter systems; Optimal control; Regulators; Riccati equations; Stability;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2006 45th IEEE Conference on

Conference_Location

San Diego, CA

Print_ISBN

1-4244-0171-2

Type

conf

DOI

10.1109/CDC.2006.377431

Filename

4177143