Parameter estimation for nonlinear time-delay systems with noisy output measurements. (October 2015)

• Record Type: Journal Article
• Authors: Lin, Qun; Loxton, Ryan; Xu, Chao; Teo, Kok Lay
• Is Part Of: Automatica. Volume 60(2015)
• Page Start: 48
• Page End: 56
• Publication Date: 2015-10
• Subjects: Time-delay -- Nonlinear system -- Parameter estimation -- Dynamic optimization -- Nonlinear optimization; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2015.06.028
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This 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.