Optimal quadratic control of linear time delay systems: One approach to numerical solution

Author

Glizer, Valery Y. ; Turetsky, Vladimir

Author_Institution

Dept. of Appl. Math., Ort Braude Coll. of Eng., Karmiel, Israel

fYear

2014

fDate

18-20 June 2014

Firstpage

797

Lastpage

802

Abstract

A finite-horizon linear-quadratic optimal control problem for systems with point-wise and distributed state delays is considered. Based on well known control optimality conditions, the solution of this problem is reduced to solution of the set of three Riccati-type matrix differential equations: an ODE and two first-order PDEs with two and three independent variables. In the paper, this set of Riccati-type equations is further reduced to a set of two equations. One of these equations is the ODE, while the other is a partial integro-differential equation. A numerical procedure of solution of this new set of equations is proposed. An illustrative example is presented.

Keywords

Riccati equations; delay systems; integro-differential equations; linear systems; matrix algebra; optimal control; partial differential equations; ODE; Riccati-type equations; Riccati-type matrix differential equations; control optimality conditions; distributed state delays; finite-horizon linear-quadratic optimal control problem; first-order PDEs; linear time delay systems; numerical procedure; numerical solution; optimal quadratic control; partial integro-differential equation; point-wise delays; Approximation methods; Computers; Delays; Differential equations; Equations; Optimal control; Symmetric matrices;

fLanguage

English

Publisher

ieee

Conference_Titel

Control & Automation (ICCA), 11th IEEE International Conference on

Conference_Location

Taichung

Type

conf

DOI

10.1109/ICCA.2014.6871023

Filename

6871023