Compositional Construction of Finite MDPs for Continuous-Time Stochastic Systems: A Dissipativity Approach

Nejati, Ameneh und Zamani, Majid (2020): Compositional Construction of Finite MDPs for Continuous-Time Stochastic Systems: A Dissipativity Approach. In: Ifac Papersonline, Bd. 53, Nr. 2: S. 1962-1967

Abstract

This paper provides a compositional scheme based on dissipativity approaches for constructing finite abstractions of continuous-time continuous-space stochastic control systems. The proposed framework enjoys the structure of the interconnection topology and employs a notion of stochastic storage functions, that describe joint dissipativity-type properties of subsystems and their abstractions. By utilizing those stochastic storage functions, one can establish a relation between continuous-time continuous-space stochastic systems and their finite counterparts while quantifying probabilistic distances between their output trajectories. Consequently, one can employ the finite system as a suitable substitution of the continuous-time one in the controller design process with a guaranteed error bound. In this respect, we first leverage dissipativity-type compositional conditions for the compositional quantification of the distance between the interconnection of continuous-time continuous-space stochastic systems and that of their discrete-time (finite or infinite) abstractions. We then consider a specific class of stochastic affine systems and construct their finite abstractions together with their corresponding stochastic storage functions. We illustrate the effectiveness of the proposed techniques by applying them to a physical case study. Copyright (C) 2020 The Authors.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Informatik
• Themengebiete: 000 Informatik, Informationswissenschaft, allgemeine Werke > 004 Informatik
• ISSN: 2405-8963
• Sprache: Englisch