We combined our knowledge to apply a direct symbolic control method to SDEs. We guarantee that solutions remain in a tube with high-proba!.
- Le Coënt, A., Fribourg, L., Vacher, J. & Wisniewski, R. Probabilistic reachability and control synthesis for stochastic switched systems using the tamed Euler method. Nonlinear Analysis: Hybrid Systems 36, 100860 (2020).
In this paper, we explain how, under the one-sided Lipschitz (OSL) hypothesis, one can find a mean square error bound for a variant of the Euler–Maruyama approximation method for stochastic switched systems. Subsequently, we explain how this bound can be used to control a stochastic switched system in order to make it reach a target zone with guaranteed minimum probability. The method is illustrated on several examples from the literature.