Adaptive Feedforward Neural Network Control With an Optimized Hidden Node Distribution

Composite adaptive radial basis function neural network (RBFNN) control with a lattice distribution of hidden nodes has three inherent demerits: 1) the approximation domain of adaptive RBFNNs is difficult to be determined a priori; 2) only a partial persistence of excitation (PE) condition can be guaranteed; 3) in general, the required number of hidden nodes of RBFNNs is enormous. This article proposes an adaptive feedforward RBFNN controller with an optimized distribution of hidden nodes to suitably address the above demerits. The distribution of the hidden nodes calculated by a K-means algorithm is optimally distributed along the desired state trajectory. The adaptive RBFNN satisfies the PE condition for the periodic reference trajectory. The weights of all hidden nodes will converge to the optimal values. This proposed method considerably reduces the number of hidden nodes, while achieving a better approximation ability. The proposed control scheme shares a similar rationality to that of the classical PID control in two special cases, which can thus be seen as an enhanced PID scheme with a better approximation ability. For the controller implemented by digital devices, the proposed method, for a manipulator with unknown dynamics, potentially achieves better control performance than model-based schemes with accurate dynamics. Simulation results demonstrate the effectiveness of the proposed scheme. This result provides a deeper insight into the coordination of the adaptive neural network control and the deterministic learning theory. Impact Statement—Adaptive RBFNN control learns to control a robot manipulator when both the structures and parameters of the target robot are unknown in advance. Unfortunately, current adaptive RBFNN controllers need a large-scale neural network to approximate the dynamics of the robot manipulator, and the learning performance cannot be guaranteed to converge. The proposed method in this article not only reduces the scale of neural networks to substantially alleviate the computational burden but also evidently achieves better learning performance. Simulation examples show that this method increases the control accuracy by more than nine times and reduces the scale of neural networks by 35 times as compared to the traditional lattice scheme. Intuitively, people usually believe that a model-based controller with an accurate dynamic model may achieve the best control performance. However, compared with the model-based controller with an accurate dynamic model, the proposed control scheme with an unknown dynamic model even further increases the control accuracy by 1.5 times. This technology provides a more straightforward path for engineers, who may be not experts in complicated control system analysis methods, to design an adaptive robotic controller to achieve enhanced performance.

I. Introduction

Adaptive radial basis function neural network (RBFNN) control is an effective way to handle uncertainties of system dynamics when both the structures and parameters are unknown [1]–[4]. RBFNNs with deterministic hidden nodes have a higher learning speed than both multilayer neural networks and RBFNNs with adjustable hidden nodes [5]. The learning mechanism of the adaptive RBFNN control with deterministic hidden nodes was named deterministic learning in [6]. Generally, there are two structures to accomplish adaptive RBFNN control: composite adaptive RBFNN control and adaptive feedforward RBFNN control.