Feedback in state constrained optimal control
ESAIM: Control, Optimisation and Calculus of Variations, Tome 7 (2002) , pp. 97-133.

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 $\epsilon >0$, produces $\epsilon$-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.

DOI : https://doi.org/10.1051/cocv:2002005
Classification : 49J24,  49J52,  49N55,  90D25
Mots clés : optimal control, state constraint, near-optimal control feedback, nonsmooth analysis
@article{COCV_2002__7__97_0,
author = {Clarke, Francis H. and Rifford, Ludovic and Stern, R. J.},
title = {Feedback in state constrained optimal control},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {97--133},
publisher = {EDP-Sciences},
volume = {7},
year = {2002},
doi = {10.1051/cocv:2002005},
zbl = {1033.49004},
mrnumber = {1925023},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2002005/}
}
Clarke, Francis H.; Rifford, Ludovic; Stern, R. J. Feedback in state constrained optimal control. ESAIM: Control, Optimisation and Calculus of Variations, Tome 7 (2002) , pp. 97-133. doi : 10.1051/cocv:2002005. http://www.numdam.org/articles/10.1051/cocv:2002005/

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