Temporally local recurrent radial basis function network for modeling and adaptive control of nonlinear systems

Abstract

In this paper, a novel temporally local recurrent radial basis function network for modeling and adaptive control of nonlinear systems is proposed. The proposed structure consists of recurrent hidden neurons having weighted self-feedback loops and a weighted linear feed-through from the input layer directly to the output layer neuron(s). The dynamic back-propagation algorithm is developed and used for updating the parameters of the proposed structure. To improve the performance of learning algorithm, discrete Lyapunov stability method is used to develop an adaptive learning rate scheme. This scheme ensures the faster convergence of the parameters and maintains the stability of the system. A total of 5 complex nonlinear systems are used to test and compare the performance of the proposed network with other neural network structures. The disturbance rejection tests are also carried out to check whether the proposed scheme is able to handle the external disturbance/noise signals effects or not. The obtained results show the efficacy of the proposed method.

Keywords: Adaptive learning rate; Dynamic back-propagation; Lyapunov stability method; Nonlinear system identification and adaptive control; Temporally local recurrent radial basis function network.