Adaptive control of nonlinear multivariable systems using neural networks

This paper considers the problem of using approximate methods for realizing the neural controllers for nonlinear multivariable systems. In [1] the NARMA-L1 and NARMA-L2 models were introduced as approximations of he NARMA model used for the representation of a SISO nonlinear dynamical systems. The advantage obtained from using NARMA-L1 and NARMA-L2 models is that control input u(k) occurs linearly and then it can be computed directly from the identification model. In contrast to the NARMA model that is not convenient for purposes of adaptive control using neural networks due to its nonlinear dependence on the control input and the training process involves dynamic gradient methods which are computationally intensive. In this paper, we take the two SISO approximate models NARMA-L1 and NARMA-L2 and extend them to be in agreement with the multivariable systems. The two new extended models are called NARMA-L3 and NARMA-L4. These two new models simplify both identification and control of the multivariable systems. In this paper we concern with the case when the system is unknown and the control has to be generated using only the values of the input and output. Simulation results are included toward the end of the paper to complement the study.