Adaptive Predictive PID Controller Based on Elman Neural Network with Hierarchical BP Algorithm

This paper presents a predictive proportional-integral-derivative (PID) controller based on Elman neural network (ENN) for a class of nonlinear systems. The ENN with both online learning and well approximation capability is employed to estimate the nonlinear function of the controlled system. The weights of the ENN identifier are trained by the hierarchical backpropagation algorithm with the adaptive learning rate, the adaptive learning rate is suitable for the ENN identifier can be convergent. The predictive PID controller is derived via a predictive performance criterion and the adaptive optimal rate for guaranteeing the convergence of the proposed PID controller. The stability analysis of the closed-loop control system is presented by the discrete Lyapunov stability theorem. Numerical simulations reveal that the proposed control law gives satisfactory tracking and disturbance rejection performances.

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