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This paper is concerned with persistent identification of systems that involve deterministic unmodeled dynamics and stochastic observation disturbances, and whose unknown parameters switch values (possibly large jumps) that can be represented by a Markov chain. Two classes of problems are considered. In the first class, the switching parameters are stochastic processes modeled by irreducible and aperiodic Markov chains with transition rates sufficiently faster than adaptation rates of the identification algorithms. In this case, tracking real-time parameters by output observations becomes impossible and we show that an averaged behavior of the parameter process can be derived from the stationary measure of the Markov chain and can be estimated with periodic inputs and least-squares type algorithms. Upper and lower error bounds are established that explicitly show impact of unmodeled dynamics. In contrast, the second class of problems represents systems whose state transitions occur infrequently. An adaptive algorithm with variable step sizes is introduced for tracking the time-varying parameters. Convergence and error bounds are derived. Numerical results are presented to illustrate the performance of the algorithm. Index Terms--Error bounds, exogenous noise, parameter switching, parameter tracking, persistent identification, unmodeled dynamics.

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. [ABSTRACT FROM AUTHOR]