Discrete Abstraction of Stochastic Nonlinear Systems

Shun-ichi AZUMA  George J. PAPPAS  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E97-A   No.2   pp.452-458
Publication Date: 2014/02/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E97.A.452
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Mathematical Systems Science and its Applications)
control,  discrete abstraction,  quantization,  stochastic systems,  

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This paper addresses the discrete abstraction problem for stochastic nonlinear systems with continuous-valued state. The proposed solution is based on a function, called the bisimulation function, which provides a sufficient condition for the existence of a discrete abstraction for a given continuous system. We first introduce the bisimulation function and show how the function solves the problem. Next, a convex optimization based method for constructing a bisimulation function is presented. Finally, the proposed framework is demonstrated by a numerical simulation.