Piecewise linear quadratic optimal control

Author

Rantzer, Anders ; Johansson, Mikael

Author_Institution

Dept. of Autom. Control, Lund Inst. of Technol., Sweden

Volume

45

Issue

4

fYear

2000

fDate

4/1/2000 12:00:00 AM

Firstpage

629

Lastpage

637

Abstract

The use of piecewise quadratic cost functions is extended from stability analysis of piecewise linear systems to performance analysis and optimal control. Lower bounds on the optimal control cost are obtained by semidefinite programming based on the Bellman inequality. This also gives an approximation to the optimal control law. An upper bound to the optimal cost is obtained by another convex optimization problem using the given control law. A compact matrix notation is introduced to support the calculations and it is proved that the framework of piecewise linear systems can be used to analyze smooth nonlinear dynamics with arbitrary accuracy

Keywords

control system analysis; linear quadratic control; linear systems; mathematical programming; matrix algebra; nonlinear control systems; stability; Bellman inequality; convex optimization problem; optimal control cost; performance analysis; piecewise linear quadratic optimal control; semidefinite programming; smooth nonlinear dynamics; stability analysis; Cost function; Linear systems; Lyapunov method; Nonlinear systems; Optimal control; Performance analysis; Piecewise linear approximation; Piecewise linear techniques; Riccati equations; Stability analysis;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.847100

Filename

847100