Approximate stochastic reachability via cascaded scenario programs: Two step analysis

Abstract

In this talk we present key characteristics of the stochastic reachability problem that make its solution particularly difficult when compared to traditional control problems. Being unable to generically solve the problem even for a single step horizon, we show how one can bound the value function using optimization methods. We present a particular method using basis functions and constraint sampling and discuss properties of the obtained solutions. We then analyse the overall structure of the presented method and identify a cascade of scenario optimization programs where the solution of one depends on the solution of the other. We formalize the properties of a solution constructed in this way and compare our results with some existing methods dealing with problems of similar structure.