Optimal state-delay control in nonlinear dynamic systems
This paper considers a class of nonlinear systems in which the control function is a time-varying state-delay. The optimal control problem is to optimize the time-varying delay and a set of time-invariant system parameters subject to lower and upper bounds. To solve this problem, we first parameteri...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Language: | English |
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PERGAMON-ELSEVIER SCIENCE LTD
2022
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| Subjects: | |
| Online Access: | http://purl.org/au-research/grants/arc/DP190103361 http://hdl.handle.net/20.500.11937/89484 |
| _version_ | 1848765229708607488 |
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| author | Liu, C. Loxton, Ryan Teo, Kok Lay Wang, Song |
| author_facet | Liu, C. Loxton, Ryan Teo, Kok Lay Wang, Song |
| author_sort | Liu, C. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | This paper considers a class of nonlinear systems in which the control function is a time-varying state-delay. The optimal control problem is to optimize the time-varying delay and a set of time-invariant system parameters subject to lower and upper bounds. To solve this problem, we first parameterize the delay in terms of piecewise-quadratic basis functions, thus yielding a finite-dimensional approximate problem with continuous-time inequality constraints induced by the delay bounds. We then exploit the quadratic structure of the delay to convert these continuous-time constraints into a finite set of canonical point constraints. We also develop an efficient numerical method for computing the gradients of the system cost function. This method, which involves integrating an auxiliary impulsive system with time-varying advance backwards in time, can be combined with any existing gradient-based optimization algorithm to generate approximate solutions for the optimal control problem. |
| first_indexed | 2025-11-14T11:31:56Z |
| format | Journal Article |
| id | curtin-20.500.11937-89484 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T11:31:56Z |
| publishDate | 2022 |
| publisher | PERGAMON-ELSEVIER SCIENCE LTD |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-894842023-06-13T05:49:20Z Optimal state-delay control in nonlinear dynamic systems Liu, C. Loxton, Ryan Teo, Kok Lay Wang, Song Science & Technology Technology Automation & Control Systems Engineering, Electrical & Electronic Engineering Delay systems Optimal control Control parameterization Numerical optimization PARAMETER-IDENTIFICATION TIME OPTIMIZATION This paper considers a class of nonlinear systems in which the control function is a time-varying state-delay. The optimal control problem is to optimize the time-varying delay and a set of time-invariant system parameters subject to lower and upper bounds. To solve this problem, we first parameterize the delay in terms of piecewise-quadratic basis functions, thus yielding a finite-dimensional approximate problem with continuous-time inequality constraints induced by the delay bounds. We then exploit the quadratic structure of the delay to convert these continuous-time constraints into a finite set of canonical point constraints. We also develop an efficient numerical method for computing the gradients of the system cost function. This method, which involves integrating an auxiliary impulsive system with time-varying advance backwards in time, can be combined with any existing gradient-based optimization algorithm to generate approximate solutions for the optimal control problem. 2022 Journal Article http://hdl.handle.net/20.500.11937/89484 10.1016/j.automatica.2021.109981 English http://purl.org/au-research/grants/arc/DP190103361 PERGAMON-ELSEVIER SCIENCE LTD restricted |
| spellingShingle | Science & Technology Technology Automation & Control Systems Engineering, Electrical & Electronic Engineering Delay systems Optimal control Control parameterization Numerical optimization PARAMETER-IDENTIFICATION TIME OPTIMIZATION Liu, C. Loxton, Ryan Teo, Kok Lay Wang, Song Optimal state-delay control in nonlinear dynamic systems |
| title | Optimal state-delay control in nonlinear dynamic systems |
| title_full | Optimal state-delay control in nonlinear dynamic systems |
| title_fullStr | Optimal state-delay control in nonlinear dynamic systems |
| title_full_unstemmed | Optimal state-delay control in nonlinear dynamic systems |
| title_short | Optimal state-delay control in nonlinear dynamic systems |
| title_sort | optimal state-delay control in nonlinear dynamic systems |
| topic | Science & Technology Technology Automation & Control Systems Engineering, Electrical & Electronic Engineering Delay systems Optimal control Control parameterization Numerical optimization PARAMETER-IDENTIFICATION TIME OPTIMIZATION |
| url | http://purl.org/au-research/grants/arc/DP190103361 http://hdl.handle.net/20.500.11937/89484 |