Persistent tracking and identification of regime‐switching systems with structural uncertainties: unmodeled dynamics, observation bias, and nonlinear model mismatch

Abstract

SUMMARYThis 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.

Parameter estimation for systems with structural uncertainties based on quantised inputs and binary‐valued output observations

“…We use a simple system to verify the theoretical results by considering where the true parameter ; the unmodelled dynamics is represented by using a finite number of terms with and , which indicates ; the observation bias and model mismatch are and , which are consistent with Assumption 2 (see [5] for details); is a sequence of i.i.d. normal random variables with zero mean and standard deviation .…”

“…Biernacki et al [4] considered the problem of robust stabilisation of a linear time‐invariant system with variations of a real parameter vector. For the systems with regime‐switching parameters, Kan et al [5] proposed a framework for persistent identification problems that encompassed many typical system uncertainties, including parameter switching, stochastic observation disturbances, deterministic unmodeled dynamics, sensor observation bias and non‐linear model mismatch. Lin et al [6] discussed the robust passivity and global stabilisation problems for a class of uncertain non‐linear stochastic systems with structural uncertainties.…”

A lifelong friendship and fruitful collaboration: A journey of more than 30 years with George Yin

“…During our collaboration and from George's frequent explanations on many of his extensive works, I have gradually figured out George's great expertise in four areas: (1) stochastic approximation; (2) regime-switching systems and switching diffusion; (3) two-time-scale Markov chains; (4) stochastic delay systems. In our joint work, George's profound knowledge and fundamental contributions in these areas have been shown in many of our papers that demonstrate integration of these system features and other added characteristics [3,22,23]. In these areas and their applications, we have served on each other's PhD student committees regularly, although we are in different colleges/schools.…”