Continuity of admissible trajectories for state constraints control problems

Authors:
  • MAM. Arisawa
    M. Arisawa
  • PLP.-L. Lions
    P.-L. Lions
Open Access
Publisher website
Google Scholar
Abstract
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.