Abstract—In this paper we propose a direct adaptive neural network control strategy for a class of unknown nonlinear systems. The adaptive controller is based on Radial Basis Function neural network. Training the RBF network as a neural model of the system using Gradient descent method initialized with unsupervised K-means clustering algorithm, control signals are directly obtained by minimizing the instant difference between a set point and the output of the Radial Basis function neural network model using the well established gradient descent rule. Since the training algorithm guarantees that the output of the RBF neural network model approaches that of the actual system, it is shown that the control signals obtained can also make the real system output close to a set point. Simulation results for both SISO and MIMO type nonlinear systems have been presented toward the end of the paper to show the validity and performance of the proposed method1.
Index Terms—Direct adaptive control, discrete-time systems, k-means clustering algorithm, MIMO systems, Radial Basis Function (RBF), SISO systems.
T. A. Alzohairy is with the Computer Science Department, Arriyadh Community College, King Saud University, Malaz, P. O. Box 28095, Riyadh 11437, Saudi Arabia. On leave from Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt (e-mail: firstname.lastname@example.org).
Cite: Tamer A. Alzohairy, "Direct Adaptive Control of Unknown Nonlinear Systems Using Radial Basis Function Networks with Gradient Descent and K-means," International Journal of Computer Theory and Engineering vol. 3, no. 6, pp. 775-784, 2011.