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Solution of a specific class of nonlinear fractional optimal control problems including multiple delays
Optimal Control Applications and Methods ( IF 1.8 ) Pub Date : 2020-08-25 , DOI: 10.1002/oca.2661 Hamid Reza Marzban 1
Optimal Control Applications and Methods ( IF 1.8 ) Pub Date : 2020-08-25 , DOI: 10.1002/oca.2661 Hamid Reza Marzban 1
Affiliation
This research provides a new framework based on a hybrid of block‐pulse functions and Legendre polynomials for the numerical examination of a special class of scalar nonlinear fractional optimal control problems involving delay. The concepts of the fractional derivative and the fractional integral are employed in the Caputo sense and the Riemann‐Liouville sense, respectively. In accordance with the notion of the Riemann‐Liouville integral, we derive a new integral operator related to the proposed basis called the operational matrix of fractional integration. By employing two significant operators, namely, the delay operator and the integral operator connected to the hybrid basis, the system dynamics of the primal optimal control problem converts to another system involving algebraic equations. Consequently, the optimal control problem under study is reduced to a static optimization one that is solved by existing well‐established optimization procedures. Some new theoretical results regarding the new basis are obtained. Various kinds of fractional optimal control problems containing delay are examined to measure the accuracy of the new method. The simulation results justify the merits and superiority of the devised procedure over the existing optimization methods in the literature.
中文翻译:
一类特殊的非线性分数最优控制问题的求解,包括多个时滞
这项研究提供了一个基于块脉冲函数和Legendre多项式混合的新框架,用于对一类特殊的涉及延迟的标量非线性分数最优控制问题进行数值检验。分数导数和分数积分的概念分别在Caputo感和Riemann-Liouville感中使用。根据Riemann-Liouville积分的概念,我们推导了一个与拟议基础有关的新积分算子,称为分数积分运算矩阵。通过使用两个重要的算子,即连接到混合基础的延迟算子和积分算子,原始最优控制问题的系统动力学转换为另一个包含代数方程的系统。所以,研究中的最优控制问题被简化为静态优化,可以通过现有完善的优化程序来解决。获得了有关新基础的一些新理论结果。研究了包含延迟的各种分数最优控制问题,以衡量新方法的准确性。仿真结果证明了所设计的方法优于文献中现有的优化方法的优点和优越性。
更新日期:2020-08-25
中文翻译:
一类特殊的非线性分数最优控制问题的求解,包括多个时滞
这项研究提供了一个基于块脉冲函数和Legendre多项式混合的新框架,用于对一类特殊的涉及延迟的标量非线性分数最优控制问题进行数值检验。分数导数和分数积分的概念分别在Caputo感和Riemann-Liouville感中使用。根据Riemann-Liouville积分的概念,我们推导了一个与拟议基础有关的新积分算子,称为分数积分运算矩阵。通过使用两个重要的算子,即连接到混合基础的延迟算子和积分算子,原始最优控制问题的系统动力学转换为另一个包含代数方程的系统。所以,研究中的最优控制问题被简化为静态优化,可以通过现有完善的优化程序来解决。获得了有关新基础的一些新理论结果。研究了包含延迟的各种分数最优控制问题,以衡量新方法的准确性。仿真结果证明了所设计的方法优于文献中现有的优化方法的优点和优越性。