An approximate dynamic programming approach to probabilistic reachability for stochastic hybrid systems

This paper addresses the computational overhead involved in probabilistic reachability computations for a general class of controlled stochastic hybrid systems. An approximate dynamic programming approach is proposed to mitigate the curse of dimensionality issue arising in the solution to the stochastic optimal control reformulation of the probabilistic reachability problem. An algorithm tailored to this problem is introduced and compared with the standard numerical solution to dynamic programming on a benchmark example.