Robust adaptive estimation of nonlinear system with time-varying parameters

• Published in: International journal of adaptive control and signal processing Vol. 29; no. 8; pp. 1055 - 1072
• Main Authors: Na, Jing, Yang, Juan, Ren, Xuemei, Guo, Yu
• Format: Journal Article
• Language: English
• Published: Bognor Regis Blackwell Publishing Ltd 01.08.2015; Wiley Subscription Services, Inc
• Subjects: adaptive system; Adaptive systems; Constants; Design engineering; Disturbances; Dynamical systems; Intervals; Nonlinear dynamics; Parameter estimation; system identification; time-varying system
• ISSN: 0890-6327; 1099-1115
• DOI: 10.1002/acs.2524

Summary The vast majority of available parameter estimation methods assume that the parameters to be estimated are constant or slowly time‐varying and mainly depend on a predictor or observer design so that a large adaptive gain must be used to achieve fast adaptation; this may result in high‐frequency oscillations when the system subjects to a large source of uncertainties or disturbances. This paper is concerned with adaptive online estimation of time‐varying parameters for two kinds of linearly parameterized nonlinear systems. By dividing the time into small intervals, the time‐varying parameters are approximated in terms of polynomials with unknown coefficients. Then a novel adaptive law design methodology is developed to estimate those constant coefficients, for which the parameter estimation error information is explicitly derived and used to drive the adaptations. To guarantee the continuity of the parameter estimation for all time, a parameter resetting scheme is introduced at the beginning of each interval. Finite‐time estimation convergence and the robustness against disturbances are all proved. Extensive simulation examples are provided to demonstrate the efficacy of the proposed algorithms for estimating time‐varying parameters. Copyright © 2014 John Wiley & Sons, Ltd.