Dynamic Analysis and Neural-Adaptive Prescribed-Time Control of the FO Memristive Magnetic-Field Electromechanical Transducer

This article is concerned with dynamic analysis and neural-adaptive prescribed-time control of the magnetic-field electromechanical transducer incorporating a memristor. First, a fractional-order (FO) mathematical model is developed, which comprehensively characterizes fractional properties of various dielectrics and establishes the relationship between magnetic flux and electric charge. The dynamical analysis explores internal evolution and complexity performance concerning a single factor or double factors among the FO, system parameter, and memristor configuration by the Bifurcation diagram, sample entropy, and complexity from multiple perspectives. Subsequently, a neural-adaptive prescribed-time control scheme is proposed to transform detrimental chaotic oscillations into orderly motions, achieve the pregiven tracking precision and accommodating both actuator fault and system uncertainty. The controller design consists of three key steps: 1) a deferred constraint function is imposed on the tracking error starting from anywhere to get assignable tracking precision within a specified time, ensuring collision avoidance; 2) a type-2 fuzzy wavelet neural network (FWNN) is utilized effectively to handle parameter perturbations and system uncertainties; and 3) a second-order FO tracking differentiator (TD) is utilized to address the "explosion of complexity" of traditional backstepping under actuator fault model. It is shown that the proposed scheme is able to ensure the boundness of all signals of the closed-loop system. Finally, extensive simulation experiments are conducted to validate the effectiveness and robustness of the rendered scheme.