Risk-Bounded Temporal Logic Control of Continuous-Time Stochastic Systems

TL;DR

This paper develops a risk-aware control synthesis method for continuous-time stochastic systems using risk signal temporal logic, reformulating risk predicates as deterministic over mean and covariance, and employing heuristics and sampled-data control for feasibility.

Contribution

It introduces a novel approach combining risk signal temporal logic with deterministic reformulation and heuristics for efficient control synthesis in stochastic systems.

Findings

Successfully bounds risk of specification violations in stochastic systems

Provides a practical control method with heuristics to manage automata complexity

Demonstrates effectiveness through simulation or case studies

Abstract

Motivated by the recent interest in risk-aware control, we study a continuous-time control synthesis problem to bound the risk that a stochastic linear system violates a given specification. We use risk signal temporal logic as a specification formalism in which distributionally robust risk predicates are considered and equipped with the usual Boolean and temporal operators. Our control approach relies on reformulating these risk predicates as deterministic predicates over mean and covariance states of the system. We then obtain a timed sequence of sets of mean and covariance states from the timed automata representation of the specification. To avoid an explosion in the number of automata states, we propose heuristics to find candidate sequences effectively. To execute and check dynamic feasibility of these sequences, we present a sampled-data control technique based on time discretization and constraint tightening that allows to perform timed transitions while satisfying the continuous-time constraints.