Approximations of stochastic hybrid systems

Approximations of stochastic hybrid systems: A compositional approach

Zamani, M (Technische Universität München)
Rungger, M (Technische Universität München)
Mohajerin Esfahani, P. (TU Delft Team Tamas Keviczky)

2017

In this paper we propose a compositional framework for the construction of approximations of the interconnection of a class of stochastic hybrid systems.
As special cases, this class of systems includes both jump linear stochastic systems and linear stochastic hybrid automata. In the proposed framework, an approximation is itself a stochastic hybrid system, which can be used as a
replacement of the original stochastic hybrid system in a controller design process. We employ a notion of so-called stochastic simulation function to quantify the error between the approximation and the original system. In the first part of the paper, we derive sufficient conditions which facilitate the compositional quantification of the error between the interconnection of stochastic hybrid subsystems and that of their approximations using the quantified error between the stochastic hybrid subsystems and their corresponding approximations. In particular, we show how to construct
stochastic simulation functions for approximations of interconnected
stochastic hybrid systems using the stochastic simulation function for the approximation of each component.
In the second part of the paper, we focus on a specific class of stochastic hybrid systems, namely, jump linear stochastic systems, and propose a constructive scheme to determine approximations together with their stochastic
simulation functions for this class of systems. Finally, we illustrate the effectiveness of the proposed results by constructing an approximation of the interconnection of four jump linear stochastic subsystems in a compositional
way.

http://resolver.tudelft.nl/uuid:919e233c-d42d-4c23-8767-cdd3877d4035

https://doi.org/10.1109/TAC.2016.2619419

0018-9286

IEEE Transactions on Automatic Control, 62 (6), 2838-2853

Accepted Author Manuscript

Institutional Repository

journal article

© 2017 M Zamani, M Rungger, P. Mohajerin Esfahani