Reach-Avoid Controllers Synthesis for Safety Critical Systems

• Published in: IEEE transactions on automatic control Vol. 69; no. 12; pp. 8892 - 8899
• Main Author: Xue, Bai
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Aerospace electronics; Control systems; Control systems design; Controllers; Differential equations; Guidance-barrier functions; Mathematical models; reach-avoid controllers; Safety; Safety critical; safety critical systems; Semidefinite programming; Stochastic processes; Stochastic systems; Synthesis; Vectors
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2024.3423837

In this article, we propose a framework for synthesizing reach-avoid controllers for deterministic systems modeled by ordinary differential equations and stochastic systems modeled by stochastic differential equations based on the notion of control guidance-barrier functions. We first consider deterministic systems and aim to synthesize a reach-avoid controller that modifies a nominal controller in a minimal way to enforce the reach-avoid objective. This objective ensures that the system enters a target set eventually while staying within an open safe set before the first target hitting time. Three control guidance-barrier functions and corresponding conditions for synthesizing reach-avoid controllers are developed. These conditions progressively weaken, facilitating optimal controller design. We then extend two of these functions for deterministic systems to stochastic systems to synthesize reach-avoid controllers in the probabilistic setting. Finally, we provide several examples to demonstrate the effectiveness of our proposed methods, using the semidefinite programming tool.