An Operator-Theoretic Framework for the Optimal Control Problem of Nonlinear Caputo Fractional Systems
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916688090365952 |
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| author | Jha, Dev Prakash George, Raju K. |
| author_facet | Jha, Dev Prakash George, Raju K. |
| contents | This paper addresses the optimal control problem for a class of nonlinear fractional systems involving Caputo derivatives and nonlocal initial conditions. The system is reformulated as an abstract Hammerstein-type operator equation, enabling the application of operator-theoretic techniques. Sufficient conditions are established to guarantee the existence of mild solutions and optimal control-state pairs. The analysis covers both convex and non-convex scenarios through various sets of assumptions on the involved operators. An optimality system is derived for quadratic cost functionals using the Gâteaux derivative, and the connection with Pontryagin-type minimum principles is discussed. Illustrative examples demonstrate the effectiveness of the proposed theoretical framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09611 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Operator-Theoretic Framework for the Optimal Control Problem of Nonlinear Caputo Fractional Systems Jha, Dev Prakash George, Raju K. Optimization and Control This paper addresses the optimal control problem for a class of nonlinear fractional systems involving Caputo derivatives and nonlocal initial conditions. The system is reformulated as an abstract Hammerstein-type operator equation, enabling the application of operator-theoretic techniques. Sufficient conditions are established to guarantee the existence of mild solutions and optimal control-state pairs. The analysis covers both convex and non-convex scenarios through various sets of assumptions on the involved operators. An optimality system is derived for quadratic cost functionals using the Gâteaux derivative, and the connection with Pontryagin-type minimum principles is discussed. Illustrative examples demonstrate the effectiveness of the proposed theoretical framework. |
| title | An Operator-Theoretic Framework for the Optimal Control Problem of Nonlinear Caputo Fractional Systems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2504.09611 |