Strategy Synthesis for Partially-known Switched Stochastic Systems

TL;DR

This paper introduces a data-driven method for synthesizing strategies in partially-known switched stochastic systems, combining Gaussian process learning, formal abstraction, and robust strategy synthesis to ensure high satisfaction probability of temporal logic specifications.

Contribution

It develops a novel framework that integrates learning, formal modeling, and robust control for partially-known stochastic systems with temporal logic goals.

Findings

Strategy synthesis is effective on linear and non-linear systems.

The approach guarantees near-optimal satisfaction probabilities.

Experimental results validate the framework's applicability and robustness.

Abstract

We present a data-driven framework for strategy synthesis for partially-known switched stochastic systems. The properties of the system are specified using linear temporal logic (LTL) over finite traces (LTLf), which is as expressive as LTL and enables interpretations over finite behaviors. The framework first learns the unknown dynamics via Gaussian process regression. Then, it builds a formal abstraction of the switched system in terms of an uncertain Markov model, namely an Interval Markov Decision Process (IMDP), by accounting for both the stochastic behavior of the system and the uncertainty in the learning step. Then, we synthesize a strategy on the resulting IMDP that maximizes the satisfaction probability of the LTLf specification and is robust against all the uncertainties in the abstraction. This strategy is then refined into a switching strategy for the original stochastic system. We show that this strategy is near-optimal and provide a bound on its distance (error) to the optimal strategy. We experimentally validate our framework on various case studies, including both linear and non-linear switched stochastic systems.