# American Institute of Mathematical Sciences

July  1996, 2(3): 297-305. doi: 10.3934/dcds.1996.2.297

## Continuity of admissible trajectories for state constraints control problems

 1 CEREMADE, URA CNRS 749, Université Paris-Dauphine, Place du Marchal de Lattre de Tassigny, 75775 Paris Cedex 16, France, France

Received  April 1996 Published  May 1996

We consider here deterministic control problems with state constraints that is problems where admissible controls are those which keep the state of the system in a given region for all times. We prove that, given an initial state and an admissible control for that state, it is possible to construct admissible controls for all initial states such that the control and the corresponding trajectory are Lipschitz (in convenient norms) with respect to the initial condition.
Citation: M. Arisawa, P.-L. Lions. Continuity of admissible trajectories for state constraints control problems. Discrete & Continuous Dynamical Systems, 1996, 2 (3) : 297-305. doi: 10.3934/dcds.1996.2.297
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