Optimal Control Problems with Mixed and Pure State Constraints
This paper provides necessary conditions of optimality for optimal control problems, in which the pathwise constraints comprise both “pure” constraints on the state variable and “mixed” constraints on control and state variables. The proofs are along the lines of earlier analysis for mixed constrain...
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| Format: | Article |
| Language: | en_US |
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Society for Industrial and Applied Mathematics
2017
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| Online Access: | http://hdl.handle.net/1721.1/110182 https://orcid.org/0000-0003-4862-5520 |
| _version_ | 1826200623523037184 |
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| author | de Pinho, M. D. R. Vinter, R. B. Boccia, Andrea |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering de Pinho, M. D. R. Vinter, R. B. Boccia, Andrea |
| author_sort | de Pinho, M. D. R. |
| collection | MIT |
| description | This paper provides necessary conditions of optimality for optimal control problems, in which the pathwise constraints comprise both “pure” constraints on the state variable and “mixed” constraints on control and state variables. The proofs are along the lines of earlier analysis for mixed constraint problems, according to which Clarke's theory of “stratified” necessary conditions is applied to a modified optimal control problem resulting from absorbing the mixed constraint into the dynamics; the difference here is that necessary conditions which now take into account the presence of pure state constraints are applied to the modified problem. Necessary conditions are given for a rather general formulation of the problem containing both forms of the constraints, and then these are specialized to problems having special structure. While combined pure state and mixed control/state problems have been previously treated in the literature, the necessary conditions in this paper are proved under less restrictive hypotheses and for novel formulations of the constraints. |
| first_indexed | 2024-09-23T11:39:19Z |
| format | Article |
| id | mit-1721.1/110182 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:39:19Z |
| publishDate | 2017 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | mit-1721.1/1101822022-10-01T05:05:31Z Optimal Control Problems with Mixed and Pure State Constraints de Pinho, M. D. R. Vinter, R. B. Boccia, Andrea Massachusetts Institute of Technology. Department of Mechanical Engineering Boccia, Andrea This paper provides necessary conditions of optimality for optimal control problems, in which the pathwise constraints comprise both “pure” constraints on the state variable and “mixed” constraints on control and state variables. The proofs are along the lines of earlier analysis for mixed constraint problems, according to which Clarke's theory of “stratified” necessary conditions is applied to a modified optimal control problem resulting from absorbing the mixed constraint into the dynamics; the difference here is that necessary conditions which now take into account the presence of pure state constraints are applied to the modified problem. Necessary conditions are given for a rather general formulation of the problem containing both forms of the constraints, and then these are specialized to problems having special structure. While combined pure state and mixed control/state problems have been previously treated in the literature, the necessary conditions in this paper are proved under less restrictive hypotheses and for novel formulations of the constraints. 2017-06-22T20:38:17Z 2017-06-22T20:38:17Z 2016-11 2015-09 Article http://purl.org/eprint/type/JournalArticle 0363-0129 1095-7138 http://hdl.handle.net/1721.1/110182 Boccia, A.; de Pinho, M. D. R. and Vinter, R. B. “Optimal Control Problems with Mixed and Pure State Constraints.” SIAM Journal on Control and Optimization 54, no. 6 (January 2016): 3061–3083 © 2016, Society for Industrial and Applied Mathematics https://orcid.org/0000-0003-4862-5520 en_US http://dx.doi.org/10.1137/15M1041845 SIAM Journal on Control and Optimization Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Society for Industrial and Applied Mathematics SIAM |
| spellingShingle | de Pinho, M. D. R. Vinter, R. B. Boccia, Andrea Optimal Control Problems with Mixed and Pure State Constraints |
| title | Optimal Control Problems with Mixed and Pure State Constraints |
| title_full | Optimal Control Problems with Mixed and Pure State Constraints |
| title_fullStr | Optimal Control Problems with Mixed and Pure State Constraints |
| title_full_unstemmed | Optimal Control Problems with Mixed and Pure State Constraints |
| title_short | Optimal Control Problems with Mixed and Pure State Constraints |
| title_sort | optimal control problems with mixed and pure state constraints |
| url | http://hdl.handle.net/1721.1/110182 https://orcid.org/0000-0003-4862-5520 |
| work_keys_str_mv | AT depinhomdr optimalcontrolproblemswithmixedandpurestateconstraints AT vinterrb optimalcontrolproblemswithmixedandpurestateconstraints AT bocciaandrea optimalcontrolproblemswithmixedandpurestateconstraints |