Guaranteed-cost controls of minimal variation: A numerical algorithm based on control parameterization
The optimal control literature is dominated by standard problems in which the system cost functional is expressed in the well-known Bolza form. Such Bolza cost functionals consist of two terms: a Mayer term (which depends solely on the final state reached by the system) and a Lagrange integral term...
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| Format: | Conference Paper |
| Published: |
IEEE
2014
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| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/42082 |
| _version_ | 1848756321595162624 |
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| author | Loxton, Ryan Lin, Qun Teo, Kok Lay |
| author2 | Shengyuan Xu |
| author_facet | Shengyuan Xu Loxton, Ryan Lin, Qun Teo, Kok Lay |
| author_sort | Loxton, Ryan |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | The optimal control literature is dominated by standard problems in which the system cost functional is expressed in the well-known Bolza form. Such Bolza cost functionals consist of two terms: a Mayer term (which depends solely on the final state reached by the system) and a Lagrange integral term (which depends on the state and control values over the entire time horizon). One limitation with the standard Bolza cost functional is that it does not consider the cost of control changes. Such costs should certainly be considered when designing practical control strategies, as changing the control signal will invariably cause wear and tear on the system’s acutators. Accordingly, in this paper, we propose a new optimal control formulation that balances system performance with control variation. The problem is to minimize the total variation of the control signal subject to a guaranteed-cost constraint that ensures an acceptable level of system performance (as measured by a standard Bolza cost functional). We first apply the control parameterization method to approximate this problem by a non-smooth dynamic optimization problem involving a nite number of decision variables. We then devise a novel transformation procedure for converting this non-smooth dynamic optimization problem into a smooth problem that can be solved using gradient-based optimization techniques. The paper concludes with numerical examples in fisheries and container crane control. |
| first_indexed | 2025-11-14T09:10:21Z |
| format | Conference Paper |
| id | curtin-20.500.11937-42082 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:10:21Z |
| publishDate | 2014 |
| publisher | IEEE |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-420822023-02-27T07:34:26Z Guaranteed-cost controls of minimal variation: A numerical algorithm based on control parameterization Loxton, Ryan Lin, Qun Teo, Kok Lay Shengyuan Xu Qianchuan Zhao Total variation Control parameterization Nonlinear optimization Optimal control The optimal control literature is dominated by standard problems in which the system cost functional is expressed in the well-known Bolza form. Such Bolza cost functionals consist of two terms: a Mayer term (which depends solely on the final state reached by the system) and a Lagrange integral term (which depends on the state and control values over the entire time horizon). One limitation with the standard Bolza cost functional is that it does not consider the cost of control changes. Such costs should certainly be considered when designing practical control strategies, as changing the control signal will invariably cause wear and tear on the system’s acutators. Accordingly, in this paper, we propose a new optimal control formulation that balances system performance with control variation. The problem is to minimize the total variation of the control signal subject to a guaranteed-cost constraint that ensures an acceptable level of system performance (as measured by a standard Bolza cost functional). We first apply the control parameterization method to approximate this problem by a non-smooth dynamic optimization problem involving a nite number of decision variables. We then devise a novel transformation procedure for converting this non-smooth dynamic optimization problem into a smooth problem that can be solved using gradient-based optimization techniques. The paper concludes with numerical examples in fisheries and container crane control. 2014 Conference Paper http://hdl.handle.net/20.500.11937/42082 IEEE fulltext |
| spellingShingle | Total variation Control parameterization Nonlinear optimization Optimal control Loxton, Ryan Lin, Qun Teo, Kok Lay Guaranteed-cost controls of minimal variation: A numerical algorithm based on control parameterization |
| title | Guaranteed-cost controls of minimal variation: A numerical algorithm based on control parameterization |
| title_full | Guaranteed-cost controls of minimal variation: A numerical algorithm based on control parameterization |
| title_fullStr | Guaranteed-cost controls of minimal variation: A numerical algorithm based on control parameterization |
| title_full_unstemmed | Guaranteed-cost controls of minimal variation: A numerical algorithm based on control parameterization |
| title_short | Guaranteed-cost controls of minimal variation: A numerical algorithm based on control parameterization |
| title_sort | guaranteed-cost controls of minimal variation: a numerical algorithm based on control parameterization |
| topic | Total variation Control parameterization Nonlinear optimization Optimal control |
| url | http://hdl.handle.net/20.500.11937/42082 |