Feedback in state constrained optimal control

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

ESAIM: Control, Optimisation and Calculus of Variations (2002)

  • 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 (2002): 97-133. <http://eudml.org/doc/244838>.

@article{Clarke2002,
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 $\varepsilon &gt;0$, produces $\varepsilon $-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},
language = {eng},
pages = {97-133},
publisher = {EDP-Sciences},
title = {Feedback in state constrained optimal control},
url = {http://eudml.org/doc/244838},
volume = {7},
year = {2002},
}

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
PY - 2002
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 $\varepsilon &gt;0$, produces $\varepsilon $-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
UR - http://eudml.org/doc/244838
ER -

References

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