Abstract

This paper develops an adaptive backstepping optimal control scheme for a fractional-order chaotic magnetic-field electromechanical transducer with the saturated control inputs. A dynamical analysis is used to check for abundant dynamical behaviors of the system by using phase diagrams and time histories under different excitations and fractional orders. A fuzzy wavelet neural network (FWNN) is utilized with an adaptive feedforward control input in order to estimate the unknown dynamical system. An auxiliary system is then developed to compensate the effects caused by the saturated control inputs, along with a tracking differentiator (TD) to realize the signal estimation associated with the fractional derivative. Taking FWNN, TD and auxiliary system into the framework of the fractional-order backstepping control, an adaptive feedforward controller is designed. In addition, we use a data-driven learning framework based on an actor critic network to solve the derived Hamilton–Jacobi–Bellman equation. The whole control policy, composing of an adaptive feedforward controller and an optimal feedback controller, not only guarantees the boundness of all signals and suppresses oscillations from the chaos and deadzone, but also makes the cost function to be smallest. Finally, the simulation results demonstrate the effectiveness of the presented scheme.

中文翻译：

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分数阶混沌磁场机电变换器的自适应反推最优控制

摘要

本文针对具有饱和控制输入的分数阶混沌磁场机电变换器，提出了一种自适应反推最优控制方案。通过使用相位图和时间历程，在不同的激励和分数阶下，使用动力学分析来检查系统的大量动力学行为。模糊小波神经网络（FWNN）与自适应前馈控制输入一起使用，以估算未知的动力学系统。然后开发一个辅助系统来补偿由饱和控制输入引起的影响，以及跟踪微分器（TD）以实现与分数导数相关的信号估计。将FWNN，TD和辅助系统纳入分数阶反推控制的框架，设计了自适应前馈控制器。此外，我们使用基于演员评论家网络的数据驱动学习框架来求解导出的汉密尔顿-雅各比-贝尔曼方程。整个控制策略由自适应前馈控制器和最优反馈控制器组成，不仅保证了所有信号的有界性，并抑制了混沌和死区引起的振荡，而且使成本函数最小。最后，仿真结果证明了所提方案的有效性。不仅保证了所有信号的有界性，并抑制了混沌和死区引起的振荡，而且使成本函数最小。最后，仿真结果证明了所提方案的有效性。不仅保证了所有信号的有界性，并抑制了混沌和死区引起的振荡，而且使成本函数最小。最后，仿真结果证明了所提方案的有效性。