Search

For subexponential random variablesXi, 1 ⩽i⩽n, the uniform asymptotic resultis established for 0

This paper studies identification of linear systems with binary-valued observations generated via fixed thresholds. In addition to stochastic measurement noises, the systems are also subject to structural uncertainties, including deterministic unmodelled dynamics, nonlinear model mismatch, and sensor observation bias. Since binary-valued observations can supply only limited information on the signals, truncated empirical measures are introduced to extract further information for system identification. An effective identification algorithm is constructed based on the proposed empirical measures. Optimal identification errors, time complexity, optimal input design, and impact of disturbances, unmodelled dynamics, observation bias, and nonlinear model mismatch are thoroughly investigated in a stochastic information framework. Asymptotic upper and lower bounds are established on identification errors. Numerical experiments are presented to demonstrate the effectiveness of the algorithms and the main results. [ABSTRACT FROM PUBLISHER]

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]

This work is concerned with identification of systems that are subject to not only measurement noises, but also structural uncertainties such as unmodeled dynamics, sensor nonlinear mismatch, and observation bias. Identification errors are analyzed for their dependence on these structural uncertainties. Asymptotic distributions of scaled sequences of estimation errors are derived. [ABSTRACT FROM AUTHOR]