Robust Control for Signal Temporal Logic Specifications using Average Space Robustness

TL;DR

This paper introduces a new robust control framework for signal temporal logic specifications that is computationally efficient and uses average space robustness, enabling convex optimization and robust satisfaction in complex multi-agent systems.

Contribution

It proposes a novel average space robustness measure integrated into a model predictive control framework, simplifying the optimization to convex quadratic programs.

Findings

Efficient control synthesis for complex temporal logic specifications.

Convex quadratic program formulation without disjunctions.

Successful simulation results on multi-agent systems.

Abstract

Control systems that satisfy temporal logic specifications have become increasingly popular due to their applicability to robotic systems. Existing control methods, however, are computationally demanding, especially when the problem size becomes too large. In this paper, a robust and computationally efficient model predictive control framework for signal temporal logic specifications is proposed. We introduce discrete average space robustness, a novel quantitative semantic for signal temporal logic, that is directly incorporated into the cost function of the model predictive controller. The optimization problem entailed in this framework can be written as a convex quadratic program when no disjunctions are considered and results in a robust satisfaction of the specification. Furthermore, we define the predicate robustness degree as a new robustness notion. Simulations of a multi-agent system subject to complex specifications demonstrate the efficacy of the proposed method.