Back-propagation neural networks in adaptive control of unknown nonlinear systems

Abstract

The objective of this research is to develop a Back-propagation Neural Network (BNN) to control certain classes of unknown nonlinear systems and explore the network's capabilities. The structure of the Direct Model Reference Adaptive Controller (DMRAC) for Linear Time Invariant (LTI) systems with unknown parameters is first analyzed. This structure is then extended using a BNN for adaptive control of unknown nonlinear systems. The specific structure of the BNN DMRAC is developed for control of four general classes of nonlinear systems modeled in discrete time. Experiments are conducted by placing a representative system from each class under the BNN's control. The condition under which the BNN DMRAC can successfully control these systems are investigated. The design and training of the BNN are also studied. The results of the experiments show that the BNN DMRAC works for the representative systems considered, while the conventional least-squares estimator DMRAC fails. Based on analysis and experimental findings, some genera conditions required to ensure that this technique works are postulated and discussed. General guidelines used to achieve the stability of the BNN learning process and good learning convergence are also discussed. To establish this as a general and significant control technique, further research is required to obtain analytically, the conditions for stability of the controlled system, and to develop more specific rules and guidelines in the BNN design and training.