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Feedback in state constrained optimal control

Published online by Cambridge University Press:  15 September 2002

Francis H. Clarke ,
Ludovic Rifford  and
R. J. Stern
Francis H. Clarke
Affiliation:
Institut Desargues, bâtiment 101, Université Claude Bernard Lyon I, 69622 Villeurbanne, France; clarke@desargues.univ-lyon1.fr.
R. J. Stern
Affiliation:
Department of Mathematics and Statistics, Concordia University, Montréal, Quebec H4B 1R6, Canada.
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Abstract

An optimal control problem is studied, in which the state is required to remain in a compact set S. A control feedback law is constructed which, for given ε > 0, produces ε-optimal trajectories that satisfy the state constraint universally with respect to all initial conditions in S. The construction relies upon a constraint removal technique which utilizes geometric properties of inner approximations of S and a related trajectory tracking result. The control feedback is shown to possess a robustness property with respect to state measurement error.

Keywords

Optimal controlstate constraintnear-optimal control feedbacknonsmooth analysis.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 7 , 2002 , pp. 97 - 133
Copyright
© EDP Sciences, SMAI, 2002

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