A NUMERICAL ALGORITHM FOR CONSTRAINED OPTIMAL CONTROL PROBLEMS
In this paper, we consider a general class of discrete-time optimal control problems subject to all-time-step constraints on the state and control variables. The derivations of the gradient formulas for the cost and constraint functions for this constrained discrete-time optimal control problem are...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
2023
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| Online Access: | http://purl.org/au-research/grants/arc/LP160100528 http://hdl.handle.net/20.500.11937/96301 |
| _version_ | 1848766131900252160 |
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| author | Zhao, B. Xu, Honglei Teo, Kok Lay |
| author_facet | Zhao, B. Xu, Honglei Teo, Kok Lay |
| author_sort | Zhao, B. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we consider a general class of discrete-time optimal control problems subject to all-time-step constraints on the state and control variables. The derivations of the gradient formulas for the cost and constraint functions for this constrained discrete-time optimal control problem are rather involved. We present a simple approach to the derivations of these gradient formulas based on reversed automatic differentiation. On this basis, a numeri- cal algorithm is developed to solve this all-time-step constrained discrete-time optimal control problem. We then consider a class of continuous-time optimal control problems subject to continuous state inequality constraints. This con- strained continuous-time optimal control problem is discretized into a discrete- time optimal control problem with all-time-step constraints using the Euler discretization method. Then, the algorithm developed for constrained discrete- time optimal control problem is applied to solve this discretized optimal control problem. Numerical examples are presented to verify the applicability of the proposed methods. |
| first_indexed | 2025-11-14T11:46:16Z |
| format | Journal Article |
| id | curtin-20.500.11937-96301 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T11:46:16Z |
| publishDate | 2023 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-963012024-11-26T00:21:57Z A NUMERICAL ALGORITHM FOR CONSTRAINED OPTIMAL CONTROL PROBLEMS Zhao, B. Xu, Honglei Teo, Kok Lay In this paper, we consider a general class of discrete-time optimal control problems subject to all-time-step constraints on the state and control variables. The derivations of the gradient formulas for the cost and constraint functions for this constrained discrete-time optimal control problem are rather involved. We present a simple approach to the derivations of these gradient formulas based on reversed automatic differentiation. On this basis, a numeri- cal algorithm is developed to solve this all-time-step constrained discrete-time optimal control problem. We then consider a class of continuous-time optimal control problems subject to continuous state inequality constraints. This con- strained continuous-time optimal control problem is discretized into a discrete- time optimal control problem with all-time-step constraints using the Euler discretization method. Then, the algorithm developed for constrained discrete- time optimal control problem is applied to solve this discretized optimal control problem. Numerical examples are presented to verify the applicability of the proposed methods. 2023 Journal Article http://hdl.handle.net/20.500.11937/96301 10.3934/jimo.2023053 http://purl.org/au-research/grants/arc/LP160100528 https://creativecommons.org/licenses/by/4.0/ fulltext |
| spellingShingle | Zhao, B. Xu, Honglei Teo, Kok Lay A NUMERICAL ALGORITHM FOR CONSTRAINED OPTIMAL CONTROL PROBLEMS |
| title | A NUMERICAL ALGORITHM FOR CONSTRAINED OPTIMAL CONTROL PROBLEMS |
| title_full | A NUMERICAL ALGORITHM FOR CONSTRAINED OPTIMAL CONTROL PROBLEMS |
| title_fullStr | A NUMERICAL ALGORITHM FOR CONSTRAINED OPTIMAL CONTROL PROBLEMS |
| title_full_unstemmed | A NUMERICAL ALGORITHM FOR CONSTRAINED OPTIMAL CONTROL PROBLEMS |
| title_short | A NUMERICAL ALGORITHM FOR CONSTRAINED OPTIMAL CONTROL PROBLEMS |
| title_sort | numerical algorithm for constrained optimal control problems |
| url | http://purl.org/au-research/grants/arc/LP160100528 http://hdl.handle.net/20.500.11937/96301 |