Solutions of Nonlinear Optimal Control Problems Using Quasilinearization and Fenchel Duality Article Swipe
Yi Li
,
Di Wu
,
Changjun Yu
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2201.07483
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2201.07483
In this paper, we consider a special class of nonlinear optimal control problems, where the control variables are box-constrained and the objective functional is strongly convex corresponding to control variables and separable with respect to the state variables and control variables. We convert solving the original nonlinear problem into solving a sequence of constrained linear-quadratic optimal control problems by quasilinearization method. In order to solve each linear-quadratic problem efficiently we turn to study its dual problem. We formulate dual problem by the scheme of Fenchel duality, the strong duality property and the saddle point property corresponding to primal and dual problem are also proved, which together ensure that solving dual problem is effective. Thus solving the sequence of control constrained linear-quadratic optimal control problems obtained by quasilinearization technique is substituted by solving the sequence of their dual problem. We solve the sequence of dual problem and obtain the solution to primal control constrained linear-quadratic problem by the saddle point property. Furthermore, the fact that solution to each subproblem finally converges to the solution to the optimality conditions of original nonlinear problem is also proved. After that we carry out numerical experiments using present approach, for each subproblem we formulate the discretized primal and dual problem by Euler discretization scheme in our experiments. Efficiency of the present method is validated by numerical results.
Related Topics
Concepts
Mathematics
Discretization
Sequence (biology)
Duality (order theory)
Optimal control
Duality gap
Mathematical optimization
Strong duality
Nonlinear system
Quadratic equation
Optimization problem
Saddle point
Applied mathematics
Mathematical analysis
Biology
Geometry
Discrete mathematics
Genetics
Physics
Quantum mechanics
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2201.07483
- https://arxiv.org/pdf/2201.07483
- OA Status
- green
- Cited By
- 2
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4221162579
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4221162579Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2201.07483Digital Object Identifier
- Title
-
Solutions of Nonlinear Optimal Control Problems Using Quasilinearization and Fenchel DualityWork title
- Type
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preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2022Year of publication
- Publication date
-
2022-01-19Full publication date if available
- Authors
-
Yi Li, Di Wu, Changjun YuList of authors in order
- Landing page
-
https://arxiv.org/abs/2201.07483Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2201.07483Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2201.07483Direct OA link when available
- Concepts
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Mathematics, Discretization, Sequence (biology), Duality (order theory), Optimal control, Duality gap, Mathematical optimization, Strong duality, Nonlinear system, Quadratic equation, Optimization problem, Saddle point, Applied mathematics, Mathematical analysis, Biology, Geometry, Discrete mathematics, Genetics, Physics, Quantum mechanicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
2Total citation count in OpenAlex
- Citations by year (recent)
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2024: 1, 2022: 1Per-year citation counts (last 5 years)
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.problem. | 75, 137 |
| abstract_inverted_index.problems | 57, 123 |
| abstract_inverted_index.property | 89, 94 |
| abstract_inverted_index.results. | 221 |
| abstract_inverted_index.sequence | 51, 116, 133, 141 |
| abstract_inverted_index.solution | 148, 164, 172 |
| abstract_inverted_index.strongly | 24 |
| abstract_inverted_index.together | 105 |
| abstract_inverted_index.approach, | 193 |
| abstract_inverted_index.converges | 169 |
| abstract_inverted_index.formulate | 77, 198 |
| abstract_inverted_index.nonlinear | 9, 46, 179 |
| abstract_inverted_index.numerical | 189, 220 |
| abstract_inverted_index.objective | 21 |
| abstract_inverted_index.problems, | 12 |
| abstract_inverted_index.property. | 159 |
| abstract_inverted_index.separable | 31 |
| abstract_inverted_index.technique | 127 |
| abstract_inverted_index.validated | 218 |
| abstract_inverted_index.variables | 16, 29, 37 |
| abstract_inverted_index.Efficiency | 212 |
| abstract_inverted_index.conditions | 176 |
| abstract_inverted_index.effective. | 112 |
| abstract_inverted_index.functional | 22 |
| abstract_inverted_index.optimality | 175 |
| abstract_inverted_index.subproblem | 167, 196 |
| abstract_inverted_index.variables. | 40 |
| abstract_inverted_index.constrained | 53, 119, 152 |
| abstract_inverted_index.discretized | 200 |
| abstract_inverted_index.efficiently | 68 |
| abstract_inverted_index.experiments | 190 |
| abstract_inverted_index.substituted | 129 |
| abstract_inverted_index.Furthermore, | 160 |
| abstract_inverted_index.experiments. | 211 |
| abstract_inverted_index.corresponding | 26, 95 |
| abstract_inverted_index.discretization | 207 |
| abstract_inverted_index.box-constrained | 18 |
| abstract_inverted_index.linear-quadratic | 54, 66, 120, 153 |
| abstract_inverted_index.quasilinearization | 59, 126 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile |