Parameter estimation for nonlinear time-delay systems with noisy output measurements
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...
| Main Authors: | , , , |
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| Format: | Journal Article |
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Pergamon Press
2015
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| Online Access: | http://hdl.handle.net/20.500.11937/5589 |
| _version_ | 1848744839180451840 |
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| author | Lin, Qun Loxton, Ryan Xu, C. Teo, Kok Lay |
| author_facet | Lin, Qun Loxton, Ryan Xu, C. Teo, Kok Lay |
| author_sort | Lin, Qun |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T06:07:50Z |
| format | Journal Article |
| id | curtin-20.500.11937-5589 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T06:07:50Z |
| publishDate | 2015 |
| publisher | Pergamon Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-55892017-10-06T00:48:11Z Parameter estimation for nonlinear time-delay systems with noisy output measurements Lin, Qun Loxton, Ryan Xu, C. Teo, Kok Lay Nonlinear system Time-delay Parameter estimation Nonlinear optimization Dynamic optimization 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. 2015 Journal Article http://hdl.handle.net/20.500.11937/5589 10.1016/j.automatica.2015.06.028 Pergamon Press fulltext |
| spellingShingle | Nonlinear system Time-delay Parameter estimation Nonlinear optimization Dynamic optimization Lin, Qun Loxton, Ryan Xu, C. Teo, Kok Lay Parameter estimation for nonlinear time-delay systems with noisy output measurements |
| title | Parameter estimation for nonlinear time-delay systems with noisy output measurements |
| title_full | Parameter estimation for nonlinear time-delay systems with noisy output measurements |
| title_fullStr | Parameter estimation for nonlinear time-delay systems with noisy output measurements |
| title_full_unstemmed | Parameter estimation for nonlinear time-delay systems with noisy output measurements |
| title_short | Parameter estimation for nonlinear time-delay systems with noisy output measurements |
| title_sort | parameter estimation for nonlinear time-delay systems with noisy output measurements |
| topic | Nonlinear system Time-delay Parameter estimation Nonlinear optimization Dynamic optimization |
| url | http://hdl.handle.net/20.500.11937/5589 |