Marzban Hamid Reza
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 84156-83111, Iran.
ISA Trans. 2023 Feb;133:233-247. doi: 10.1016/j.isatra.2022.06.037. Epub 2022 Jun 30.
We aim to develop a direct transcription approach for solving a notable category of optimal control problems governed by nonlinear fractional Fredholm integral equations having delays in both input and output signals. The foundation of the new methodology is based on a multi domains decomposition scheme by utilizing the fractional-order Legendre functions. A new fractional derivative operator associated with the fractional basis is introduced by using the Caputo fractional derivative operator. With the use of derivative and delay operators, one can transform the dynamical system related to the fractional control problem into a new system containing algebraic equations. A wide variety of challenging test problems are studied to provide a detailed explanation of the designed approach.
我们旨在开发一种直接转录方法，用于解决由输入和输出信号均具有延迟的非线性分数阶Fredholm积分方程所支配的一类显著的最优控制问题。新方法的基础是利用分数阶勒让德函数的多域分解方案。通过使用Caputo分数阶导数算子，引入了一个与分数阶基相关的新分数阶导数算子。利用导数和延迟算子，可以将与分数阶控制问题相关的动态系统转化为一个包含代数方程的新系统。研究了各种具有挑战性的测试问题，以详细解释所设计的方法。
