From Small-Gain Theory to Compositional Construction of Barrier Certificates for Large-Scale Stochastic Systems

• 成果类型: Article
• 署名作者: Anand, Mahathi; Lavaei, Abolfazl; Zamani, Majid
• 署名单位: University of Munich; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Colorado System; University of Colorado Boulder
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3183032
• 发表日期: 2022
• 页码: 5638-5645
• 关键词: Compositionality; control barrier certificates; finite-state automata; formal controller synthesis; large-scale stochastic systems; small-gain conditions

摘要

This article is concerned with a compositional approach for the construction of control barrier certificates for large-scale interconnected stochastic systems while synthesizing hybrid controllers against high-level logic properties. Our proposed methodology involves decomposition of interconnected systems into smaller subsystems and leverages the notion of control sub-barrier certificates of subsystems, enabling one to construct control barrier certificates of interconnected systems by employing some max-type small-gain conditions. The main goal is to synthesize hybrid controllers enforcing complex logic properties, including the ones represented by the accepting language of deterministic finite automata, while providing probabilistic guarantees on the satisfaction of given specifications in bounded-time horizons. To do so, we propose a systematic approach to first decompose high-level specifications into simple reachability tasks by utilizing automata corresponding to the complement of specifications. We then construct control sub-barrier certificates and synthesize local controllers for those simpler tasks and combine them to obtain a hybrid controller that ensures satisfaction of the complex specification with some lower bound on the probability of satisfaction. We finally apply our proposed techniques to a fully-interconnected Kuramoto network composed of 100 nonlinear oscillators.