Adaptive backstepping optimal control of a fractional-order chaotic magnetic-field electromechanical transducer

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.