Bisimilar symbolic models for stochastic control systems without state-space discretization
Majid Zamani, Ilya Tkachev, Alessandro Abate · 2014
In the past few years different techniques have been developed for constructively deriving symbolic abstractions of (stochastic) control systems. The obtained symbolic models allow us to leverage the apparatus of finite-state reactive synthesis towards the problem of designing hybrid controllers enforcing rich logic specifications over the concrete models. Unfortunately, most of the existing techniques severely suffer from the curse of dimensionality due to the need to discretize state and input sets. In this paper we provide a symbolic abstraction technique for incrementally stable stochastic control systems, which only requires discretizing input sets. We show that for every incrementally stable stochastic control system, and for every given positive precision ε, the discretization of exclusively the input set allows constructing a symbolic model which is ε-approximate bisimilar (in moments) to the original stochastic control system. The details of the proposed technique are elucidated by synthesizing a control policy for a 6-dimensional linear stochastic control system satisfying some logic specifications, which would not be tractable using existing approaches based on state-space discretization.