Automata-based controller synthesis for stochastic systems: A game framework via approximate probabilistic relations

Zhong, Bingzhuo; Lavaei, Abolfazl; Zamani, Majid und Caccamo, Marco (2022): Automata-based controller synthesis for stochastic systems: A game framework via approximate probabilistic relations. In: Automatica, Bd. 147

Abstract

In this work, we propose an abstraction and refinement methodology for the controller synthesis of discrete-time stochastic systems to enforce complex logical properties expressed by deterministic finite automata (a.k.a. DFA). Our proposed scheme is based on a notion of so-called (epsilon, 8)-approximate probabilistic relations, allowing one to quantify the similarity between stochastic systems modeled by discrete-time stochastic games and their corresponding finite abstractions. Leveraging this type of relations, the lower bound for the probability of satisfying the desired specifications can be well ensured by refining controllers synthesized over abstract systems to the original games. Moreover, we propose an algorithmic procedure to construct such a relation for a particular class of nonlinear stochastic systems with slope restrictions on the nonlinearity. The proposed methods are demonstrated on a quadrotor example, and the results indicate that the desired lower bound for the probability of satisfaction is guaranteed.(c) 2022 Elsevier Ltd. All rights reserved.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Informatik
• Themengebiete: 000 Informatik, Informationswissenschaft, allgemeine Werke > 004 Informatik
• ISSN: 0005-1098
• Sprache: Englisch