Policy Synthesis for Switched Linear Systems with Markov Decision Process Switching
Abstract
We study the synthesis of mode switching protocols for a class of discrete-time switched linear systems in which the mode jumps are governed by Markov decision processes (MDPs). We call such systems MDP-JLS for brevity. Each state of the MDP corresponds to a mode in the switched system. The probabilistic state transitions in the MDP represent the mode transitions. We focus on finding a policy that selects the switching actions at each mode such that the switched system that follows these actions is guaranteed to be stable. Given a policy in the MDP, the considered MDP-JLS reduces to a Markov jump linear system (MJLS). {We consider both mean-square stability and stability with probability one. For mean-square stability, we leverage existing stability conditions for MJLSs and propose efficient semidefinite programming formulations to find a stabilizing policy in the MDP. For stability with probability one, we derive new sufficient conditions and compute a stabilizing policy using linear programming. We also extend the policy synthesis results to MDP-JLS with uncertain mode transition probabilities.
Cite
@article{arxiv.2001.00835,
title = {Policy Synthesis for Switched Linear Systems with Markov Decision Process Switching},
author = {Bo Wu and Murat Cubuktepe and Franck Djeumou and Zhe Xu and Ufuk Topcu},
journal= {arXiv preprint arXiv:2001.00835},
year = {2020}
}
Comments
arXiv admin note: text overlap with arXiv:1904.11456