Abstract This paper investigates the issues of dynamical analysis and accelerated adaptive stabilization of the fractional-order (FO) centrifugal flywheel governor system with optimality. The dynamic behavior of the centrifugal flywheel governor system is revealed and its local stability is discussed in the fractional calculus (FC). A speed function is introduced to accelerate convergence rate within a pre-given time and a hierarchical type-2 fuzzy neural network (HT2FNN) is employed to play an approximating role for unknown nonlinear items. An extended state tracking differentiator which overcomes repetitive differentiation problem is used to approximate the derivative of virtual control input. Then, a stabilization controller is designed by integrating with the speed function, neural network and tracking differentiator in the framework of backstepping. It is proved that the proposed scheme guarantees the boundedness of all signals of the closed-loop system by using the frequency distributed model and makes the predefined cost function smallest. Finally, simulation results verify the effectiveness of the presented scheme.

中文翻译：

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分数阶离心飞轮调速器系统动力学分析及其优化加速自适应镇定

摘要 本文研究了分数阶（FO）离心式飞轮调速器系统优化的动力学分析和加速自适应稳定问题。揭示了离心飞轮调速器系统的动态行为，并在分数阶微积分 (FC) 中讨论了其局部稳定性。引入速度函数以在给定时间内加快收敛速度​​，并采用分层类型 2 模糊神经网络 (HT2FNN) 对未知非线性项起到逼近作用。克服重复微分问题的扩展状态跟踪微分器用于近似虚拟控制输入的导数。然后，结合速度函数设计稳定控制器，反推框架中的神经网络和跟踪微分器。证明该方案利用频率分布模型保证了闭环系统所有信号的有界性，并使预定义的代价函数最小。最后，仿真结果验证了所提出方案的有效性。