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

This paper presents an application of TimeDelay adaptive neural networks based on a dynamic neural network for trajectory tracking of unknown nonlinear plants. Our approach is based on two main methodologies: the first one employs Time-Delay neural networks and Lyapunov-Krasovskii functions and the second 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 Synchronization. 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.