Guaranteed Control of Sampled Switched Systems Using Semi-Lagrangian Schemes and One-Sided Lipschitz Constants

Adrien Le Coent1, Laurent Fribourg2

  • 1Aalborg University
  • 2CNRS

Details

11:00 - 11:20 | Wed 11 Dec | Rhodes CD | WeA17.4

Session: Switched Systems I

Abstract

In this paper, we propose a new method for ensuring formally that a controlled trajectory stays inside a given safety set S for a given duration T. Using a finite gridding X of S, we first synthesize, for a subset of initial nodes x of X, an admissible control for which the Euler-based approximate trajectories lie in S at t ∈ [0,T]. We then give sufficient conditions which ensure that the exact trajectories, under the same control, also lie in S for t ∈ [0,T], when starting at initial points “close” to nodes x. The statement of such conditions relies on results giving estimates of the deviation of Euler-based approximate trajectories, using one-sided Lipschitz constants. We illustrate the interest of the method on several examples, including a stochastic one.