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ESAIM: Control, Optimisation and Calculus of Variations (1)

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Feedback in state constrained optimal control
Francis H. Clarke, Ludovic Rifford, R. J. Stern
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 7 / 2002

Published online by Cambridge University Press:

15 September 2002, pp. 97-133

Print publication:

2002
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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.