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Persistent tracking and identification of regime‐switching systems with structural uncertainties: unmodeled dynamics, observation bias, and nonlinear model mismatch
Author(s) -
Kan Shaobai,
Yin George,
Wang Le Yi
Publication year - 2013
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.2288
Subject(s) - nonlinear system , aperiodic graph , control theory (sociology) , markov chain , identification (biology) , probabilistic logic , computer science , tracking (education) , estimation theory , stochastic process , markov process , system identification , process (computing) , mathematics , algorithm , artificial intelligence , statistics , data modeling , control (management) , psychology , pedagogy , physics , botany , combinatorics , quantum mechanics , machine learning , database , biology , operating system
SUMMARY This work focuses on tracking and system identification of systems with regime‐switching parameters, which are modeled by a Markov process. It introduces a framework for persistent identification problems that encompass many typical system uncertainties, including parameter switching, stochastic observation disturbances, deterministic unmodeled dynamics, sensor observation bias, and nonlinear model mismatch. In accordance with the ‘frequency’ of the parameter switching process, we divide the problems into two classes. For fast‐switching systems, the switching parameters are stochastic processes modeled by irreducible and aperiodic Markov chains. Because accurately tracking real‐time parameters in such systems is not possible because of the uncertainty principles, the effect of parameter switching is evaluated on their average by the stationary distribution of the Markovian chain and estimated by the least squares algorithms. We derive upper and lower bounds on identification errors, which characterize how identification accuracy depends on the earlier uncertainty terms. When the system parameters switch their values infrequently in a probabilistic sense, their values can be tracked based on input/output observations. Stochastic approximation algorithms with adaptive step sizes are used for such systems. Simulation studies are carried out to demonstrate that slowly varying parameters could be tracked with reasonable accuracy.Copyright © 2012 John Wiley & Sons, Ltd.