2017/09/29 by Abolfazl Lavaei, Sadegh Soudjani, Lavaei, Abolfazl +5
Biochemistry, Genetics and Molecular Biology · Engineering · #Advanced Control Systems Optimization #Control Systems and Identification #FOS: Electrical engineering #Fault Detection and Control Systems #Gene Regulatory Network Analysis #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1709.10312
openalex publication_date 2017/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is concerned with a compositional approach for constructing\nabstractions of interconnected discrete-time stochastic control systems. The\nabstraction framework is based on new notions of so-called stochastic\nsimulation functions, using which one can quantify the distance between\noriginal interconnected stochastic control systems and their abstractions in\nthe probabilistic setting. Accordingly, one can leverage the proposed results\nto perform analysis and synthesis over abstract interconnected systems, and\nthen carry the results over concrete ones. In the first part of the paper, we\nderive sufficient small-gain type conditions for the compositional\nquantification of the distance in probability between the interconnection of\nstochastic control subsystems and that of their abstractions. In the second\npart of the paper, we focus on the class of discrete-time linear stochastic\ncontrol systems with independent noises in the abstract and concrete\nsubsystems. For this class of systems, we propose a computational scheme to\nconstruct abstractions together with their corresponding stochastic simulation\nfunctions. We demonstrate the effectiveness of the proposed results by\nconstructing an abstraction (totally 4 dimensions) of the interconnection of\nfour discrete-time linear stochastic control subsystems (together 100\ndimensions) in a compositional fashion.\n