Probabilistic reachability and control synthesis for stochastic switched systems using the tamed Euler method.

14 Jan 2020 in Publications

with A. Le Coënt, L. Fribourg and R. Wisniewski.

We combined our knowledge to apply a direct symbolic control method to SDEs. We guarantee that solutions remain in a tube with high-proba!.

1. 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).

   @article{lecoent2020probabilistic,
     title = {Probabilistic reachability and control synthesis for stochastic switched systems using the tamed Euler method},
     author = {Le Co\"ent, Adrien and Fribourg, Laurent and Vacher, Jonathan and Wisniewski, Rafael},
     journal = {Nonlinear Analysis: Hybrid Systems},
     volume = {36},
     pages = {100860},
     year = {2020},
     publisher = {Elsevier},
     doi = {10.1016/j.nahs.2020.100860}
   }
   

Abstract

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.