SySCoRe 2.0: Toolset for formal control synthesis of continuous-state stochastic systems and temporal logic specifications

Abstract

We present SySCoRe 2.0, a MATLAB toolset that synthesizes controllers for stochastic systems to satisfy temporal logic specifications. Starting from a system description and a co-safe temporal logic specification, SySCoRe provides all necessary functions for synthesizing a robust controller and quantifying the associated formal robustness guarantees. It distinguishes itself from other available tools by supporting both stochastic model order reduction techniques and space discretizations, and by being applicable to nonlinear dynamics and complex co-safe temporal logic specifications over infinite horizons. To achieve this, SySCoRe generates a finite abstraction from a possibly reduced-order version of the provided model and performs probabilistic model checking. Then, it establishes a probabilistic coupling between the original model and its finite abstraction encoded in an approximate simulation relation, based on which a lower bound on the satisfaction probability is computed. The error computed by SySCoRe does not grow linearly in the horizon of the specification, thus it provides non-trivial lower bounds for infinite-horizon specifications and unbounded disturbances. SySCoRe exploits a tensor representation to facilitate an efficient computation of transition probabilities in the finite abstraction. We showcase these features on several benchmarks and compare the performance of the toolset with existing tools and with the previous version of SySCoRe.