Robust Estimation of Higher Order Derivatives of Solutions to Some Nonlinear Systems Under Uncertainties

Abstract

Estimation of derivatives of a noisy signal is a practically important problem which frequently is approached via application of different filtering methodologies. Our work focuses on estimating of derivatives of solutions to partly unknown nonlinear systems subject to bounded system and measurement noises. The robust observers are designed to approximate higher order derivatives for some nonlinear systems arising in various application domains and to estimate numerically the accuracy of such approximations. We also determine how the estimation errors are in influenced by measurement and system noises and disclose amplification of the error norm is due to increased observer gains. Consequently, we use estimations of derivatives to forecast the system dynamics on relatively short time intervals.