Towars a Theory of Stochastic Hybrid Systems
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Probabilistic reachability and safety for controlled discrete time stochastic hybrid systems
Automatica (Journal of IFAC)
Reachability questions in piecewise deterministic Markov processes
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
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The generalized class of stochastic hybrid systems consists of models with regime changes including the occurrence of impulsive behavior. In this paper, the stochastic hybrid processes with jumps are approximated by locally consistent Markov decision processes that preserve local mean and covariance. We further apply a randomized switching policy for approximating the dynamics on the switching boundaries. To investigate the validity of the approximation, we study a stochastic optimal control problem. On the basis of the discrete approximation, we solve the optimal control problem and show that the solution obtained from the discretized problem converges to the solution of the original optimal control problem.