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arXiv · 1903.05882

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

Adrien Le Coënt·Laurent Fribourg
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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 $\in$ [0,T]. We then give sufficient conditions which ensure that the exact trajectories, under the same control, also lie in S for t $\in$ [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.

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Adrien Le Coënt, Laurent Fribourg. 2019-03-14. Guaranteed Control of Sampled Switched Systems using Semi-Lagrangian Schemes and One-Sided Lipschitz Constants. https://arxiv.org/abs/1903.05882

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