Novel General Regression Neural Networks for Improving Control Accuracy of Nonlinear MIMO Discrete-Time Systems

In this article, a novel version of the general regression neural network (Imp_GRNN) is developed to control a class of multiinput and multioutput (MIMO) nonlinear discrete-time (DT) systems. The improvements retain the features of the original GRNN along with a significant improvement of the control accuracy. The enhancements include developing a method to set the input-hidden weights of GRNN using the inputs recursive statistical means, introducing a new output layer and adaptable forward weighted connections from the inputs to the new layer, and suggesting an interval-type smoothing parameter to eradicate the need for selecting the parameter beforehand or adapting it online. Also, controller stability is studied using Lyapunov's method for DT systems. The controller performance is tested with different simulation examples and compared with the original GRNN to verify its superiority over it. Also, Imp_GRNN performance is compared with an adaptive radial basis function network controller, an adaptive feedforward neural-network (NN) controller, and a proportional-integral-derivative (PID) controller, where it demonstrated higher accuracy in comparison with them. In comparison with the formerly proposed control methods for MIMO DT systems, our controller is capable of producing high control accuracy while it is model free, does not require complex mathematics, has low computational complexity, and can be utilized for a wide range of DT dynamic systems. Also, it is one of the few methods that aims to improve the control system accuracy by improving the NN structure.