In this paper, a novel method is presented for optimal control of fractional order systems in the presence of an unknown term in system dynamic where fractional order derivative is considered to be between zero and one. In this method, neural network is used to estimate the unknown term in system dynamic. Neural network coefficients are updated adaptively and online. Updating laws are presented considering system requirements to achieve a homogeneous fractional order system. Another problem is formulating optimal control laws for fractional order system which is solved through fractional differential calculus. Since optimal fractional order control is non-causal and does not have a online solution, step-by-step progression and predictive control idea are used to obtain control signal and combine optimal controller and estimator. This method results in an optimal run-time control and resolves unknown terms in system dynamic. In addition, the closed loop system being uniform ultimate bounded is proved through direct Lyapunov method. Finally, simulation results are given to show efficiency of the proposed method.

中文翻译：

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基于神经估计器的分数阶不确定非线性连续时间系统最优控制

在本文中，提出了一种新颖的方法，用于在系统动力学中存在未知项的情况下最优控制分数阶系统，其中分数阶导数被视为介于零和一之间。在这种方法中，使用神经网络来估计系统动态中的未知项。神经网络系数可以自适应地在线更新。提出了考虑系统要求以实现齐次分数阶系统的更新定律。另一个问题是制定分数阶系统的最优控制律，这是通过分数微分法解决的。由于最优分数阶控制是无因的，并且没有在线解决方案，因此采用逐步进行和预测控制的思想来获得控制信号，并将最优控制器和估计器组合在一起。此方法可实现最佳的运行时控制，并解决系统动态中的未知项。另外，通过直接李雅普诺夫方法证明了具有统一极限极限的闭环系统。最后，仿真结果表明了该方法的有效性。