PID Control Law for Trajectory Tracking Error Using Time-Delay Adaptive Neural Networks for Chaos Synchronization

This paper presents an application of Time- Delay adaptive neural networks based on a dynamic neural network for trajectory tracking of unknown nonlin- ear plants. Our approach is based on two main method- ologies: the first one employs Time-Delay neural net- works and Lyapunov-Krasovskii functions and the sec- ond one is Proportional-Integral-Derivative (PID) control for nonlinear systems. The proposed controller structure is composed of a neural identifier and a control law defined by using the PID approach. The new control scheme is applied via simulations to Chaos Synchroniza- tion. Experimental results have shown the usefulness of the proposed approach for Chaos Production. To verify the analytical results, an example of a dynamical network is simulated and a theorem is proposed to ensure the tracking of the nonlinear system.