Almost invariant manifold approach for adaptive estimation of periodic and aperiodic unknown time‐varying parameters

This paper provides a novel identification technique for the estimation of time‐varying parameters in a class of nonlinear dynamical systems. The concept of almost invariant manifold is used to find an implicit mapping from known variables of the system to the unknown variables. A parameter estimation update law is generated from the proposed mapping. The exponential convergence of parameter estimation error to a small neighbourhood of the origin is achieved. The algorithm is extended to estimate the uncertain periodic parameters. An upper bound estimation of the unknown periodic parameters and their time derivatives are obtained. Unlike most periodic time‐varying parameter estimation techniques, only the knowledge of the number of distinctive frequencies is assumed. The effectiveness of the proposed method is illustrated with two simulation examples. Copyright © 2015 John Wiley & Sons, Ltd.