Feedback in state constrained optimal control
Institut Desargues, bâtiment 101,
Université Claude Bernard Lyon I, 69622 Villeurbanne, France; email@example.com.
2 Department of Mathematics and Statistics, Concordia University, Montréal, Quebec H4B 1R6, Canada.
Revised: 2 July 2001
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.
Mathematics Subject Classification: 49J24 / 49J52 / 49N55 / 90D25
Key words: Optimal control / state constraint / near-optimal control feedback / nonsmooth analysis.
© EDP Sciences, SMAI, 2002