Model-Predictive Control of Discrete Hybrid Stochastic Automata

This paper focuses on optimal and receding horizon control of a class of hybrid dynamical systems, called Discrete Hybrid Stochastic Automata (DHSA), whose discrete-state transitions depend on both deterministic and stochastic events. A finite-time optimal control approach "optimistically" determines the trajectory that provides the best tradeoff between tracking performance and the probability of the trajectory to actually execute, under possible chance constraints. The approach is also robustified, less optimistically, to ensure that the system satisfies a set of constraints for all possible realizations of the stochastic events, or alternatively for those having enough probability to realize. Sufficient conditions for asymptotic convergence in probability are given for the receding-horizon implementation of the optimal control solution. The effectiveness of the suggested stochastic hybrid control techniques is shown on a case study in supply chain management.