Mixed structured RBF network for direct inverse control of nonlinear systems

In this paper, a novel radial basis function (RBF) neural network is proposed and applied successively for online stable identification and control of nonlinear discrete-time systems. The proposed RBF network has one hidden layer neural network (NN) with its all parameters being adaptable. The RBF network parameters are optimized by gradient descent method with stable learning rate whose stable convergence behavior is proved by Lyapunov stability approach. The aim of construction of the proposed RBF network is to combine power of the networks which have different mapping abilities. These networks are auto-regressive exogenous input model, nonlinear static NN model and nonlinear dynamic NN model. In simulations, the proposed network is applied for the direct inverse control of one benchmark nonlinear functioned system and Van de Vusse reaction in a CSTR discrete system even there exist large disturbances. From simulations, it is seen that the RBF network with stable learning rate identifies and controls nonlinear systems accurately.