Robust parameter estimation for constrained time-delay systems with inexact measurements

Abstract

<p style='text-indent:20px;'>In this paper, we consider estimation problems involving constrained nonlinear systems with the unknown time-delays and unknown system parameters. These unknown quantities are to be estimated such that a least-squares error function between the system output and a set of noisy measurements is minimized subject to the characteristic time constraints specifying the restrictions. We first present the classical estimation formulation, where the expectation of the error function is regarded as the cost function. Then, in order to obtain robust estimates against the noises in measurements, we propose a robust estimation formulation, in which the cost function is the variance of the error function and an additional constraint indicates an allowable sacrifice from the optimal expectation value of the classical estimation problem. For these two estimation problems, we derive the gradients of the corresponding cost and constraint functions with respect to time-delays and system parameters by solving some auxiliary time-delay systems backward in time. On this basis, we develop gradient-based optimization algorithms to determine the optimal time-delays and system parameters. Finally, we consider two example problems, including a parameter estimation problem in microbial batch fermentation process, to illustrate the effectiveness and applicability of our proposed algorithms.