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

• Qun Lin ^[1] ; Ryan Loxton ^[1] ; Chao Xu ^[2] ; Kok Lay Teo ^[1]
  1. [1] Curtin University

     Curtin University

     Australia

     
  2. [2] Zhejiang University

     Zhejiang University

     China

     
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 60, 2015, págs. 48-56
• Idioma: inglés
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• Resumen

  • 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.