A Specification-Guided Framework for Temporal Logic Control of Nonlinear Systems

• 成果类型: Article
• 署名作者: Li, Yinan; Sun, Zhibing; Liu, Jun
• 署名单位: University of Waterloo
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3168489
• 发表日期: 2023
• 页码: 2002-2017
• 关键词: automata; Heuristic algorithms; Aerospace electronics; Random access memory; PLANNING; control systems; Memory management; formal methods; interval analysis; linear temporal logic (LTL); nonlinear control

摘要

This article proposes a specification-guided framework for control of nonlinear systems with linear temporal logic (LTL) specifications. In contrast with well-known abstraction-based methods, the proposed framework directly characterizes the winning set, i.e., the set of initial conditions from which a given LTL formula can be realized, over the continuous state space of the system via a monotonic operator. Following this characterization, an algorithm is proposed to practically approximate the operator via an adaptive interval subdivision scheme, which yields a finite-memory control strategy. We show that the proposed algorithm is sound for full LTL specifications, and robustly complete for specifications recognizable by deterministic Buchi automaton (DBA), the latter in the sense that control strategies can be found whenever the given specification can be satisfied with additional bounded disturbances. Without having to compute and store the abstraction and the resulting product system with the DBA, the proposed method is more memory efficient, which is demonstrated by complexity analysis and performance tests. A preprocessing stage is also devised to reduce computational cost via a decomposition of the specification. We show that the proposed method can effectively solve real-world control problems, such as jet engine compressor control and motion planning for manipulators and mobile robots.