Summary: An approximate dynamic programming approach
to probabilistic reachability for stochastic hybrid systems
Alessandro Abate, Maria Prandini, John Lygeros, and Shankar Sastry
Abstract-- 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.
Stochastic Hybrid Systems (SHS) are a general class of
models relevant to a wide range of application contexts
involving interacting discrete and continuous dynamics, as
well as probabilistic uncertainty, , .
In this paper we study the reachability problem for SHS.
Reachability is an important topic in systems theory. Quali-
tatively, it deals with the issue of evaluating whether the state