Regulation of Nonlinear Dynamical Systems Using Multiple Neural Networks

The paper introduces two new concepts which are found to be effective in the regulation of unknown dynamical systems around desired points in the state space. The first deals with the use of multiple neural networks for the representation of a nonlinear system to overcome the inherent problem of nonuniform distribution of the input data. The second is a successive identification and control procedure which enables the desired region in the state space to be explored in a stable fashion. Both classes of problems addressed are generic in the control of dynamical systems using neural networks and the solutions proposed have wide applications. The paper considers low order dynamical systems in which the control input enters additively. In view of the nonlinear nature of the plant, precise analytic statements can be made at present only for first order systems. However, the concepts are applicable to higher order systems and simulation results are provided for second order systems to demonstrate the effectiveness of the method proposed. Several open questions and directions are discussed towards the end of the paper.