Analysis of the Zhang Neural Network and its Application for the control of Nonlinear Dynamical Systems

摘要

This research article presents a development of the Zhang Recurrent Neural Network (Z-RNN) model to estimate the on-line solution to linear time-varying matrix equations. This Z-RNN model is further used to develop a control strategy for nonlinear systems by estimating the solution to a Lyapunov equation on-line, without approximations and linearization. The proposed concept is validated using a 4th order Inverted Pendulum on a Cart model and it has been compared with the Linear Quadratic Regulator. The proposed technique offers a significantly lower cost and better performance. The issues with stability of the Z-RNN and sampling rate is also discussed in detail, along with the choice of parameters involved.