Recurrent Neural Networks in Linear Systems Controlling Patic P. C.*, Zemouri R.**, Duta L.* *Valahia University of Târgovişte, 18-24, Unirii Ave., Târgovişte, Romania (patic@valahia.ro, duta@valahia.ro) **Laboratoire d’Automatique du CNAM, 21, Rue Pinel, 75013 Paris, France (ryad.zemouri@cnam.fr) Abstract. This paper presents an application of an ANN (Artificial Neural Network) of a RNRF type (Recurrent Network with Radial basis Function) in controlling a linear system. The performance of ANN-based control solution is compared with a classic controller and the results show that ANN behaves better than the classic controller. MATLAB simulation performed show that the coupling between the ANN and a proportional controller gives the best performance. 1 Introduction The linear systems control is today an important research and development area in control engineering. In the real world, however, many processes are characterized by a nonlinear dynamic behavior which make impossible to use conventional tools for automatic control. The same applies to systems for which mathematical models are incompletely specified or of a poor quality. There is currently no systematic theory to be applied to control such processes. To solve this problem, one solution is to use a learning phase to identify the process model or controller. The term "learning" is about changing the structure and/or system settings in order to improve its future performance, based on previous experimental observations [1]. Some adaptive controlling methods have been developed, to enable the evolution of controller depending on the task [3], [11]. The structure of the controller being already chosen, those methods allow fixing a number of parameters of this one. If the general principle used by these algorithms is similar to learning done by ANN, adaptation is done by a simple setting of a small number of coefficients of the control loop without storage capacity [5]. Systems with learning characteristics such as ANN (Artificial Neural Networks) can be successfully utilized in control problems such as the decision support or situation recognition [4], [6]. In this case we speak about learning in command rather than adaptive control. This article consists of three parts. Section I reviews a dynamic variation of ANN that one of the authors of this paper proposed in a previous work [21]. Section II presents the basic principles and some methods of neurons control technique. Finally, Section III presents the tests and the obtained experimental results. 2 Recurrent Neural Networks The used neural network is a variant of dynamic networks radial basis functions of dynamic RNRF: Recurrent Neural Networks with Radial Basis Function [19]. The RNRF considers the time as an internal parameter of the network [2], [5]. This dynamical aspect is obtained by a recurrence of connections between neurons of the input layer. These self connections provide the input neurons a capacity for taking into account of past input data. The neural network is equipped with two types of memories: a dynamic memory, for taking into account the dynamic data input and a static memory to store prototypes. The output layer represents the layer of Gaussian weighting [13]. fonctions Sigmoïdes Fonctions Gaussiennes Neurone de Sortie I 1 I 2 Ii S w11 w22 wii W1 W2 Wj Wn Fig. 1. RNRF network Each neuron from the input layer performs an addition at time t of its input () i I t and at the output of the preceding time ( 1) i xt  weighted by the coefficient of self-connection ii w [17]. The neuron outputs the result of the activation function: () ( 1) () i ii i i at wxt It      () () i i xt f at  (1)