Adaptive online estimation of time-varying parameter nonlinear systems

This paper addresses adaptive online estimation of time-varying parameters for a class of linearly parameterized nonlinear systems. By dividing time into small intervals, polynomials with unknown coefficients are adopted to approximate time-varying parameters within each local interval. Then a novel adaptive law for parameter estimation is developed to estimate the unknown constant coefficients of polynomials, for which the parameter estimation error is explicitly derived in terms of filter operations and used to drive the adaptations. A resetting scheme is used at the beginning of each time interval to guarantee the continuity of parameter estimation. The error convergence and the robustness against bounded external disturbances are all proved. Simulation results are included to demonstrate the effectiveness of the proposed algorithm for time-varying parameters.