Feedback in state constrained optimal control

Clarke, Francis H.; Rifford, Ludovic; Stern, R. J.

doi:10.1051/cocv:2002005

Clarke, Francis H. ; Rifford, Ludovic ; Stern, R. J.

ESAIM: Control, Optimisation and Calculus of Variations, Tome 7 (2002), pp. 97-133.

Résumé

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.

MR Zbl | 1 citation dans Numdam

DOI : 10.1051/cocv:2002005

Classification : 49J24, 49J52, 49N55, 90D25
Mots clés : optimal control, state constraint, near-optimal control feedback, nonsmooth analysis

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     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},
     mrnumber = {1925023},
     zbl = {1033.49004},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/cocv:2002005/}
}

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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://archive.numdam.org/articles/10.1051/cocv:2002005/

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