Guaranteed Control of Sampled Switched Systems using Semi-Lagrangian Schemes and One-Sided Lipschitz Constants
Abstract
In this paper, we propose a new method for ensuring formally that a controlled trajectory stay 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.
Keywords
Cite
@article{arxiv.1903.05882,
title = {Guaranteed Control of Sampled Switched Systems using Semi-Lagrangian Schemes and One-Sided Lipschitz Constants},
author = {Adrien Le Coënt and Laurent Fribourg},
journal= {arXiv preprint arXiv:1903.05882},
year = {2019}
}