A Stackelberg Game Approach for Signal Temporal Logic Control Synthesis with Uncontrollable Agents

作     者：Cui, Bohan Yu, Xinyi Giua, Alessandro Yin, Xiang 

作者机构：Department of Automation Key Laboratory of System Control and Information Processing Shanghai Jiao Tong University Shanghai200240 China Thomas Lord Department of Computer Science University of Southern California Los AngelesCA90089 United States Department of Electrical and Electronic Engineering University of Cagliari Cagliari09123 Italy 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2025年

核心收录：

主　　题：Control system synthesis 

摘      要：In this paper, we investigate the control synthesis problem for Signal Temporal Logic (STL) specifications in the presence of uncontrollable agents. Existing works mainly address this problem in a robust control setting by assuming the uncontrollable agents are adversarial and accounting for the worst-case scenario. While this approach ensures safety, it can be overly conservative in scenarios where uncontrollable agents have their own objectives that are not entirely opposed to the system’s goals. Motivated by this limitation, we propose a new framework for STL control synthesis within the Stackelberg game setting. Specifically, we assume that the system controller, acting as the leader, first commits to a plan, after which the uncontrollable agents, acting as followers, take a best response based on the committed plan and their own objectives. Our goal is to synthesize a control sequence for the leader such that, for any rational followers producing a best response, the leader’s STL task is guaranteed to be satisfied. We present an effective solution to this problem by transforming it into a single-stage optimization problem and leveraging counterexample guided synthesis techniques. We demonstrate that the proposed approach is sound and identify conditions under which it is optimal. Simulation results are also provided to illustrate the effectiveness of the proposed framework. © 2025, CC BY.