Feedback in state constrained optimal control

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

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 7, page 97-133
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Clarke, Francis H., Rifford, Ludovic, and Stern, R. J.. "Feedback in state constrained optimal control." ESAIM: Control, Optimisation and Calculus of Variations 7 (2010): 97-133. <http://eudml.org/doc/90638>.

@article{Clarke2010,
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. },
author = {Clarke, Francis H., Rifford, Ludovic, Stern, R. J.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Optimal control; state constraint; near-optimal control feedback; nonsmooth analysis.; optimal control; near-optimal control feedback; nonsmooth analysis},
language = {eng},
month = {3},
pages = {97-133},
publisher = {EDP Sciences},
title = {Feedback in state constrained optimal control},
url = {http://eudml.org/doc/90638},
volume = {7},
year = {2010},
}

TY - JOUR
AU - Clarke, Francis H.
AU - Rifford, Ludovic
AU - Stern, R. J.
TI - Feedback in state constrained optimal control
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 7
SP - 97
EP - 133
AB - 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.
LA - eng
KW - Optimal control; state constraint; near-optimal control feedback; nonsmooth analysis.; optimal control; near-optimal control feedback; nonsmooth analysis
UR - http://eudml.org/doc/90638
ER -

References

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