Mixed structured RBF network for direct inverse control of nonlinear systems

Abstract

I selami.bevhan@ege.edu.tr , 2 musa.alcirmege.edu.tr Radial Basis Function NetworksRadial basis function neural networks (RBFNNs) are the one of the different functionalized type of NNs with high approximation and regularization capability [3]. The RBFs are preferred as the basic structure of neural networks because of their good local specialization and global generalization ability [4]. The design of a RBFN in its most basic form consists of three separate layers. The first layer is the input layer. The second layer is the hidden layer and it is structured with high dimension to provide better approximation. The last layer gives the output of the network. There exist nonlinear transformation between the input layer and hidden layer. However, from hidden layer to the output layer it is linear transformation [2]. There are used some radial basis functions as functions of RBFNNs such that Gaussian RBFs, multiquadratic RBFs, inverse multiquadratic RBFs, thin plate splines RBFs, cubic splines RBFs, linear splines RBFs. However, Gausssian RBFs are employed frequently, since it is bounded, strictly positive and continuous on 9t.[2]. Moreover, they are known with noise suppression properties [5]. So in this study, Gaussian RBFs are utilized in the network.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 autoregressive 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 leaming rate identifies and controls nonlinear systems accurately.

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“…Let the constraint set Ω w be as defined in (8). If the initial values of the parameters satisfy W (0) ∈ Ω w , then the adaptation law (9) and (10) guarantees that W (k) ∈ Ω w for each time index k.…”

“…Neural networks are applied for inverse control of nonlinear systems in many works [8][9][10][11]. Consider a nonlinear system with the function of lagged input and output terms which can be formulated as…”

A hybrid algorithm based on neural network for DO concentration control

“…Although the learning method has achieved many successes in the neural control of nonlinear systems. In [10], a novel radial basis function (RBF) neural network is proposed and applied successively for online stable identification and control of nonlinear discrete-time systems. In [11], the regularization RBF neural networks for nonlinear system modeling.…”