Switching time and parameter optimization in nonlinear switched systems with multiple time-delays
Abstract In this paper, we consider a dynamic optimization problem involving a general switched system that evolves by switching between several subsystems of nonlinear delay-differential equations. The optimization variables in this system consist of: (1) the times at which the subsystem switches o...
| Main Authors: | , , |
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| Format: | Journal Article |
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Springer
2014
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| Online Access: | http://hdl.handle.net/20.500.11937/47016 |
| _version_ | 1848757719005134848 |
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| author | Liu, C. Loxton, Ryan Teo, Kok Lay |
| author_facet | Liu, C. Loxton, Ryan Teo, Kok Lay |
| author_sort | Liu, C. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | Abstract In this paper, we consider a dynamic optimization problem involving a general switched system that evolves by switching between several subsystems of nonlinear delay-differential equations. The optimization variables in this system consist of: (1) the times at which the subsystem switches occur; and (2) a set of system parameters that influence the subsystem dynamics. We first establish the existence of the partial derivatives of the system state with respect to both the switching times and the system parameters. Then, on the basis of this result, we show that the gradient of the cost function can be computed by solving the state system forward in timefollowed by a costate system backward in time. This gradient computation procedure can be combined with any gradient-based optimization method to determine the optimal switching times and parameters. We propose an effective optimization algorithm based on this idea. Finally, we consider three numerical examples, one involving the 1,3-propanediol fed-batch production process, to illustrate the effectiveness and applicability of the proposed algorithm. |
| first_indexed | 2025-11-14T09:32:33Z |
| format | Journal Article |
| id | curtin-20.500.11937-47016 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:32:33Z |
| publishDate | 2014 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-470162019-02-19T05:35:07Z Switching time and parameter optimization in nonlinear switched systems with multiple time-delays Liu, C. Loxton, Ryan Teo, Kok Lay Switched system Switching times Time-delay system Nonlinear optimization Abstract In this paper, we consider a dynamic optimization problem involving a general switched system that evolves by switching between several subsystems of nonlinear delay-differential equations. The optimization variables in this system consist of: (1) the times at which the subsystem switches occur; and (2) a set of system parameters that influence the subsystem dynamics. We first establish the existence of the partial derivatives of the system state with respect to both the switching times and the system parameters. Then, on the basis of this result, we show that the gradient of the cost function can be computed by solving the state system forward in timefollowed by a costate system backward in time. This gradient computation procedure can be combined with any gradient-based optimization method to determine the optimal switching times and parameters. We propose an effective optimization algorithm based on this idea. Finally, we consider three numerical examples, one involving the 1,3-propanediol fed-batch production process, to illustrate the effectiveness and applicability of the proposed algorithm. 2014 Journal Article http://hdl.handle.net/20.500.11937/47016 10.1007/s10957-014-0533-7 Springer fulltext |
| spellingShingle | Switched system Switching times Time-delay system Nonlinear optimization Liu, C. Loxton, Ryan Teo, Kok Lay Switching time and parameter optimization in nonlinear switched systems with multiple time-delays |
| title | Switching time and parameter optimization in nonlinear switched systems with multiple time-delays |
| title_full | Switching time and parameter optimization in nonlinear switched systems with multiple time-delays |
| title_fullStr | Switching time and parameter optimization in nonlinear switched systems with multiple time-delays |
| title_full_unstemmed | Switching time and parameter optimization in nonlinear switched systems with multiple time-delays |
| title_short | Switching time and parameter optimization in nonlinear switched systems with multiple time-delays |
| title_sort | switching time and parameter optimization in nonlinear switched systems with multiple time-delays |
| topic | Switched system Switching times Time-delay system Nonlinear optimization |
| url | http://hdl.handle.net/20.500.11937/47016 |