Optimal Control of Discrete Hybrid Stochastic Automata

This paper focuses on hybrid systems whose discrete state transitions depend on both deterministic and stochastic events. For such systems, after introducing a suitable hybrid model called Discrete Hybrid Stochastic Automaton (DHSA), different finite-time optimal control approaches are examined: (1) Stochastic Hybrid Optimal Control (SHOC), which “optimistically” determines the trajectory providing the best trade off between the tracking performance and the probability that stochastic events realize as expected, under specified chance constraints; (2) Robust Hybrid Optimal Control (RHOC) which, in addition, less optimistically, ensures that the system remains within a specified safety region for all possible realizations of stochastic events. Sufficient conditions for the asymptotic convergence of the state vector are given for receding-horizon implementations of the above schemes. The proposed approaches are exemplified on a simple benchmark problem in production system management.