Polynomial Recurrent Neural Network-Based Adaptive PID Controller with Stable Learning Algorithm

This paper introduces a novel structure of a polynomial weighted output recurrent neural network (PWORNN) for designing an adaptive proportional—integral—derivative (PID) controller. The proposed adaptive PID controller structure based on a polynomial weighted output recurrent neural network (APID-PWORNN) is introduced. In this structure, the number of tunable parameters for the PWORNN only depends on the number of hidden neurons and it is independent of the number of external inputs. The proposed structure of the PWORNN aims to reduce the number of tunable parameters, which reflects on the reduction of the computation time of the proposed algorithm. To guarantee the stability, the optimization, and speed up the convergence of the tunable parameters, i.e., output weights, the proposed network is trained using Lyapunov stability criterion based on an adaptive learning rate. Moreover, by applying the proposed scheme to a nonlinear mathematical system and the heat exchanger system, the robustness of the proposed APID-PWORNN controller has been investigated in this paper and proven its superiority to deal with the nonlinear dynamical systems considering the system parameters uncertainties, disturbances, set-point change, and sensor measurement uncertainty.