Efficient STL Control Synthesis under Asynchronous Temporal Robustness Constraints

TL;DR

This paper introduces an efficient control synthesis method for time-critical systems that ensures robustness against asynchronous timing uncertainties, using a novel approach to handle complex temporal logic specifications.

Contribution

It proposes a new optimization-based control synthesis technique under Asynchronous Temporal Robustness constraints, avoiding combinatorial complexity by leveraging instant-shift pair sets.

Findings

Method guarantees specification satisfaction within ATR bounds

Reduces computational complexity compared to naive approaches

Validated through multiple illustrative case studies

Abstract

In time-critical systems, such as air traffic control systems, it is crucial to design control policies that are robust to timing uncertainty. Recently, the notion of Asynchronous Temporal Robustness (ATR) was proposed to capture the robustness of a system trajectory against individual time shifts in its sub-trajectories. In a multi-robot system, this may correspond to individual robots being delayed or early. Control synthesis under ATR constraints is challenging and has not yet been addressed. In this paper, we propose an efficient control synthesis method under ATR constraints which are defined with respect to simple safety or complex signal temporal logic specifications. Given an ATR bound, we compute a sequence of control inputs so that the specification is satisfied by the system as long as each sub-trajectory is shifted not more than the ATR bound. We avoid combinatorially exploring all shifted sub-trajectories by first identifying redundancy between them. We capture this insight by the notion of instant-shift pair sets, and then propose an optimization program that enforces the specification only over the instant-shift pair sets. We show soundness and completeness of our method and analyze its computational complexity. Finally, we present various illustrative case studies.