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

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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.

DOI : 10.1051/cocv:2002005
Classification : 49J24, 49J52, 49N55, 90D25
Keywords: 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://geodesic.mathdoc.fr/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

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