In this paper, an optimal control scheme with known final time is presented for continuous time fractional order nonlinear systems with an unknown term in the dynamics of the system. Fractional derivative is considered based on Caputo concept and fractional order is between 0 and 1. First, a neural network observer with fractional order dynamics is designed to estimate system states. Weights of the neural network are updated adaptively and the update laws are presented as equations of fractional order. By using the Lyapunov method, it is shown that state estimation error and weight estimation error are limited. Then, the optimal control problem with known final time for fractional order nonlinear systems is presented based on observed states. Finally, the simulation results show efficiency of the proposed method.

在本文中，针对系统动力学中一个未知项的连续时间分数阶非线性系统，提出了一种具有最终时间已知的最优控制方案。基于Caputo概念考虑分数阶导数，分数阶在0到1之间。首先，设计具有分数阶动力学的神经网络观察器以估计系统状态。自适应地更新神经网络的权重，并将更新定律表示为分数阶方程。通过使用李雅普诺夫方法，表明状态估计误差和权重估计误差是有限的。然后，基于观测到的状态，给出了分数阶非线性系统具有已知最终时间的最优控制问题。最后，仿真结果表明了该方法的有效性。