Publication
A Pontryagin maximum principle for optimal control problems involving generalized distributional-order derivatives
| Summary: | In this work, we extended fractional optimal control (OC) theory by proving a version of Pontryagin’s maximum principle and establishing sufficient optimality conditions for an OC problem. The dynamical system constraint in the OC problem under investigation is described by a generalized fractional derivative: the left-sided Caputo distributed-order fractional derivative with an arbitrary kernel. This approach provides a more versatile representation of dynamic processes, accommodating a broader range of memory effects and hereditary properties inherent in diverse physical, biological, and engineering systems. |
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| Main Authors: | Cruz, Fátima |
| Other Authors: | Almeida, Ricardo miguel; Martins, Natália |
| Subject: | Fractional calculus Fractional optimal control Pontryagin maximum principle |
| Year: | 2025 |
| Country: | Portugal |
| Document type: | article |
| Access type: | open access |
| Associated institution: | Universidade de Aveiro |
| Language: | English |
| Origin: | RIA - Repositório Institucional da Universidade de Aveiro |
| Summary: | In this work, we extended fractional optimal control (OC) theory by proving a version of Pontryagin’s maximum principle and establishing sufficient optimality conditions for an OC problem. The dynamical system constraint in the OC problem under investigation is described by a generalized fractional derivative: the left-sided Caputo distributed-order fractional derivative with an arbitrary kernel. This approach provides a more versatile representation of dynamic processes, accommodating a broader range of memory effects and hereditary properties inherent in diverse physical, biological, and engineering systems. |
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