Distributionally robust parameter identification of a time-delay dynamical system with stochastic measurements
In this paper, we consider a parameter identification problem involving a time-delay dynamical system, in which the measured data are stochastic variable. However, the probability distribution of this stochastic variable is not available and the only information we have is its first moment. This pro...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Published: |
Elsevier
2019
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| Online Access: | http://purl.org/au-research/grants/arc/DP160102819 http://hdl.handle.net/20.500.11937/74842 |
| _version_ | 1848763387944632320 |
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| author | Gong, Z. Liu, C. Teo, Kok Lay Sun, Jie |
| author_facet | Gong, Z. Liu, C. Teo, Kok Lay Sun, Jie |
| author_sort | Gong, Z. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we consider a parameter identification problem involving a time-delay dynamical system, in which the measured data are stochastic variable. However, the probability distribution of this stochastic variable is not available and the only information we have is its first moment. This problem is formulated as a distributionally robust parameter identification problem governed by a time-delay dynamical system. Using duality theory of linear optimization in a probability space, the distributionally robust parameter identification problem, which is a bi-level optimization problem, is transformed into a single-level optimization problem with a semi-infinite constraint. By applying problem transformation and smoothing techniques, the semi-infinite constraint is approximated by a smooth constraint and the convergence of the smooth approximation method is established. Then, the gradients of the cost and constraint functions with respect to time-delay and parameters are derived. On this basis, a gradient-based optimization method for solving the transformed problem is developed. Finally, we present an example, arising in practical fermentation process, to illustrate the applicability of the proposed method. |
| first_indexed | 2025-11-14T11:02:40Z |
| format | Journal Article |
| id | curtin-20.500.11937-74842 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T11:02:40Z |
| publishDate | 2019 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-748422022-10-27T04:49:56Z Distributionally robust parameter identification of a time-delay dynamical system with stochastic measurements Gong, Z. Liu, C. Teo, Kok Lay Sun, Jie In this paper, we consider a parameter identification problem involving a time-delay dynamical system, in which the measured data are stochastic variable. However, the probability distribution of this stochastic variable is not available and the only information we have is its first moment. This problem is formulated as a distributionally robust parameter identification problem governed by a time-delay dynamical system. Using duality theory of linear optimization in a probability space, the distributionally robust parameter identification problem, which is a bi-level optimization problem, is transformed into a single-level optimization problem with a semi-infinite constraint. By applying problem transformation and smoothing techniques, the semi-infinite constraint is approximated by a smooth constraint and the convergence of the smooth approximation method is established. Then, the gradients of the cost and constraint functions with respect to time-delay and parameters are derived. On this basis, a gradient-based optimization method for solving the transformed problem is developed. Finally, we present an example, arising in practical fermentation process, to illustrate the applicability of the proposed method. 2019 Journal Article http://hdl.handle.net/20.500.11937/74842 10.1016/j.apm.2018.09.040 http://purl.org/au-research/grants/arc/DP160102819 http://purl.org/au-research/grants/arc/DP190103361 Elsevier fulltext |
| spellingShingle | Gong, Z. Liu, C. Teo, Kok Lay Sun, Jie Distributionally robust parameter identification of a time-delay dynamical system with stochastic measurements |
| title | Distributionally robust parameter identification of a time-delay dynamical system with stochastic measurements |
| title_full | Distributionally robust parameter identification of a time-delay dynamical system with stochastic measurements |
| title_fullStr | Distributionally robust parameter identification of a time-delay dynamical system with stochastic measurements |
| title_full_unstemmed | Distributionally robust parameter identification of a time-delay dynamical system with stochastic measurements |
| title_short | Distributionally robust parameter identification of a time-delay dynamical system with stochastic measurements |
| title_sort | distributionally robust parameter identification of a time-delay dynamical system with stochastic measurements |
| url | http://purl.org/au-research/grants/arc/DP160102819 http://purl.org/au-research/grants/arc/DP160102819 http://hdl.handle.net/20.500.11937/74842 |