Accelerated Adaptive Fuzzy Optimal Control of Three Coupled Fractional-Order Chaotic Electromechanical Transducers

Abstract

In this article, we investigate the issue of the accelerated adaptive fuzzy optimal control of three coupled fractional-order chaotic electromechanical transducers. A small network where every transducer has the nearest-neighbor coupling configuration is used to form the coupled fractional-order chaotic electromechanical transducers. The mathematical model of the coupled electromechanical transducers with nearest-neighbors is established and the dynamical analysis reveals that its behaviors are very sensitive to external excitation and fractional order. In the controller design, the recurrent nonsingleton type-2 sequential fuzzy neural network (RNT2SFNN) with the transformation is designed to estimate unknown functions of dynamics system in the feedforward fuzzy controller, and it is constructed to approximate the critic value and actor control functions by using policy iteration (PI) in the optimal feedback controller. Meanwhile, the speed functions are employed to achieve accelerated convergence within a pregiven finite time and a tracking differentiator is used to solve the explosion of terms associated with traditional backstepping. The whole control strategy consists of a feedforward controller integrating with the RNT2SFNN, tracking differentiator, and speed function in the framework of the backstepping control and a feedback controller fusing with the RNT2SFNN and PI under an actor/critic structure to solve the Hamilton–Jacobi–Bellman equation. The proposed scheme not only guarantees the boundness of all signals and realizes the chaos suppression, synchronization, and accelerated convergence, but also minimizes the cost function. Simulations demonstrate and validate the effectiveness of the proposed scheme.