Parameter estimation for nonlinear time-delay systems with noisy output measurements

Abstract

a b s t r a c tThis paper considers the problem of using noisy output data to estimate unknown time-delays and unknown system parameters in a general nonlinear time-delay system. We formulate the problem as a dynamic optimization problem in which the unknown quantities are decision variables to be chosen optimally, with the cost function penalizing the mean and variance of the least-squares error between actual and predicted system output. Since the time-delays and system parameters influence the cost function implicitly through the governing time-delay system, the cost function's gradient -which is required to solve the problem using gradient-based optimization techniques -cannot be computed analytically using standard differentiation rules. We instead develop two computational methods for evaluating this gradient: one involves solving an auxiliary time-delay system forward in time; the other involves solving an auxiliary time-advance system backward in time. On this basis, we propose an efficient optimization algorithm for determining optimal estimates for the time-delays and system parameters. We conclude the paper by examining the performance of this algorithm on a dynamic model of a continuously-stirred tank reactor.

Insulin injections and exercise scheduling for individuals with diabetes: An optimal control model

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Parameter estimation for Ginzburg-Landau equation via implicit sampling

“…We will deal with the system (4)- (6) in the rest of the paper. Since (4)-(6) can be viewed as gray-box system, one of the first issues we must face before solving the control and stabilize problems is how to identify the coefficients of system accurately [4].…”

“…subject to system (4)- (6).B(x, t) is a set of transformed observation data [7]. Using this traditional optimization method we actually can only derive the most likely parameters with the observation data which may contain some noise.…”

“…In general, various numerical methods can be used to estimate the parameters. One is to formulate the problem as a dynamic optimization problem in which the unknown quantities are decision variables to be chosen optimally [6], i.e., solving the following optimal problem…”