Abel-Gaid, S.H.; Qamlo, A.H.; Mohamed, B.G. Bang-Bang Property and Time-Optimal Control for Caputo Fractional Differential Systems. Fractal and Fractional 2024, 8, 84, doi:10.3390/fractalfract8020084.
Abel-Gaid, S.H.; Qamlo, A.H.; Mohamed, B.G. Bang-Bang Property and Time-Optimal Control for Caputo Fractional Differential Systems. Fractal and Fractional 2024, 8, 84, doi:10.3390/fractalfract8020084.
Abel-Gaid, S.H.; Qamlo, A.H.; Mohamed, B.G. Bang-Bang Property and Time-Optimal Control for Caputo Fractional Differential Systems. Fractal and Fractional 2024, 8, 84, doi:10.3390/fractalfract8020084.
Abel-Gaid, S.H.; Qamlo, A.H.; Mohamed, B.G. Bang-Bang Property and Time-Optimal Control for Caputo Fractional Differential Systems. Fractal and Fractional 2024, 8, 84, doi:10.3390/fractalfract8020084.
Abstract
Fractional differential systems have received much attention in recent decades likely due to its powerful ability in modeling memory processes, which are mostly observed in real world. Fractional models have been widely investigated and applied in many fields such as physics, biochemistry, electrical engineering, continuum and statistical mechanics. It is shown by many researchers that fractional derivatives can provide more accurate models than integer order derivatives do. Obviously, bang-bang property is of a significant importance in optimal control theory. In this paper a Bang-Bang property and time-optimal control problem for time-Fractional Differential System (FDS) is under consideration. First we formulate our problem and we prove the existence theorem. We state and prove the bang-bang theorem. Finally we give the optimality conditions that characterized the optimal control. Some illustrate applications are given to clarify our results.
Keywords
Time optimal control problems; Bang Bang Theorem; Fractional optimal control; Dirichlet parabolic equations; Classical control theory; Optimality conditions; Riemann-Liouville and Caputo's derivatives
Subject
Computer Science and Mathematics, Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
