Distributionally Robust Control for Chance-Constrained Signal Temporal Logic Specifications

TL;DR

This paper develops a distributionally robust control method for stochastic linear systems with chance constraints specified by signal temporal logic, ensuring reliability despite unknown disturbance distributions.

Contribution

It introduces a Wasserstein-metric-based approach to handle unknown disturbance distributions in STL chance-constrained control problems, providing probabilistic guarantees.

Findings

Method guarantees chance constraint satisfaction with user-defined confidence.

Approach effectively handles unknown disturbance distributions.

Numerical example demonstrates practical efficacy.

Abstract

We consider distributionally robust optimal control of stochastic linear systems under signal temporal logic (STL) chance constraints when the disturbance distribution is unknown. By assuming that the underlying predicate functions are Lipschitz continuous and the noise realizations are drawn from a distribution having a concentration of measure property, we first formulate the underlying chance-constrained control problem as stochastic programming with constraints on expectations and propose a solution using a distributionally robust approach based on the Wasserstein metric. We show that by choosing a proper Wasserstein radius, the original chance-constrained optimization can be satisfied with a user-defined confidence level. A numerical example illustrates the efficacy of the method.