Identification and Control of Nonlinear Systems Using Nonlinearly Parameterized Arnn

In this paper, a new algorithm is described for on-line identification and adaptive control of MIMO affine nonlinear systems having unknown dynamics a priori, by using a nonlinearly parameterized additive recurrent neural network (ARNN). The ARNN uses the radial basis functions (RBF) as activation functions. However, some adjustable parameters (centers and variances) in RBF appear nonlinearly and the determination of the adaptive law for such parameters is a nontrivial task. Then, we propose a new method in order to determine the training laws of all the RBF and ARNN parameters which allow to reduce the identification and control error for tracking tasks of time trajectories. Additionally, the system is augmented with sliding control to offset the higher-order terms in the Taylor series of RBF output. Such a development is necessary for the linearization of the RBF with respect to the parameters and, therefore, to obtain the training laws of the ARNN. The study of the total system stability is based on the Lyapunov theory. The theoretical results are verified through simulations executed on a simple nonlinear system.