Optimal Control Problems with Vector-Valued Impulse Controls and Time Delays
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arXiv
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| Format: | Preprint |
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2024
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| author | Fusco, Giovanni Motta, Monica Vinter, Richard |
| author_facet | Fusco, Giovanni Motta, Monica Vinter, Richard |
| contents | We consider a nonlinear control system with vector-valued measures as controls and with dynamics depending on time delayed states. First, we introduce a notion of discontinuous, bounded variation solution associated with this system and establish an equivalent representation formula for it, inspired by the approach known in delay-free impulsive control as the `graph completions' method. Then, thanks to this equivalent formulation, we prove well-posedness properties of these solutions and also derive necessary optimality conditions in the form of a Maximum Principle for an associated minimization problem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_17342 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal Control Problems with Vector-Valued Impulse Controls and Time Delays Fusco, Giovanni Motta, Monica Vinter, Richard Optimization and Control 49N25, 93C43, 49K21, 26A45, 49J21 We consider a nonlinear control system with vector-valued measures as controls and with dynamics depending on time delayed states. First, we introduce a notion of discontinuous, bounded variation solution associated with this system and establish an equivalent representation formula for it, inspired by the approach known in delay-free impulsive control as the `graph completions' method. Then, thanks to this equivalent formulation, we prove well-posedness properties of these solutions and also derive necessary optimality conditions in the form of a Maximum Principle for an associated minimization problem. |
| title | Optimal Control Problems with Vector-Valued Impulse Controls and Time Delays |
| topic | Optimization and Control 49N25, 93C43, 49K21, 26A45, 49J21 |
| url | https://arxiv.org/abs/2408.17342 |