Publicação
Time-fractional optimal control of initial value problems on time scales
| Resumo: | We investigate Optimal Control Problems (OCP) for fractional systems involving fractional-time derivatives on time scales. The fractional-time derivatives and integrals are considered, on time scales, in the Riemann–Liouville sense. By using the Banach fixed point theorem, sufficient conditions for existence and uniqueness of solution to initial value problems described by fractional order differential equations on time scales are known. Here we consider a fractional OCP with a performance index given as a delta-integral function of both state and control variables, with time evolving on an arbitrarily given time scale. Interpreting the Euler–Lagrange first order optimality condition with an adjoint problem, defined by means of right Riemann–Liouville fractional delta derivatives, we obtain an optimality system for the considered fractional OCP. For that, we first prove new fractional integration by parts formulas on time scales. |
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| Autores principais: | Bahaa, Gaber M. |
| Outros Autores: | Torres, Delfim F. M. |
| Assunto: | Fractional derivatives and integrals on time scales Initial value problems Optimal control |
| Ano: | 2019 |
| País: | Portugal |
| Tipo de documento: | capítulo de livro |
| Tipo de acesso: | acesso restrito |
| Instituição associada: | Universidade de Aveiro |
| Idioma: | inglês |
| Origem: | RIA - Repositório Institucional da Universidade de Aveiro |
| Resumo: | We investigate Optimal Control Problems (OCP) for fractional systems involving fractional-time derivatives on time scales. The fractional-time derivatives and integrals are considered, on time scales, in the Riemann–Liouville sense. By using the Banach fixed point theorem, sufficient conditions for existence and uniqueness of solution to initial value problems described by fractional order differential equations on time scales are known. Here we consider a fractional OCP with a performance index given as a delta-integral function of both state and control variables, with time evolving on an arbitrarily given time scale. Interpreting the Euler–Lagrange first order optimality condition with an adjoint problem, defined by means of right Riemann–Liouville fractional delta derivatives, we obtain an optimality system for the considered fractional OCP. For that, we first prove new fractional integration by parts formulas on time scales. |
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