Computationally Efficient Control of Nonlinear Systems Using Orthonormal Activation Function Based Neural Networks

Abstract

The application of Orthonormal Activation Function Neural Networks (OAFNN) for control of unknown, nonlinear dynamic systems is investigated. The 'inverse model control' scheme as well as 'direct adaptive control' scheme are implemented and discussed. The efficient learning capability of OAFNNs is demonstrated and compared with other popular sigmoid and functional link networks using a Training Error Convergence Cost (TECC) function. The controllers exploit the 'stable learning1, 'no local minimum' and 'fast convergence' properties of OAFNN. The properties of OAFNNs are presented. The weights in direct adaptive controller are tuned on-line. The tracking error is shown to be bounded using Lyapunov theory. The OAFNN weights arc shown to be bounded using properties of orthogonal functions. The simplicity of the structure of OAFNN based controllers besides their fast parameter convergence capability, allows computationally efficient controllers, as compared to the existing Neural Network (NN) controllers.