Fractional Order PID Control Law for Trajectory Tracking Using Fractional Order Time-Delay Recurrent Neural Networks for Fractional Order Complex Dynamical Systems

Abstract

In this paper presents an extension to the theory on the analysisof stability of complex systems with time delay of fractionalorder, the previous study is based on the theory of functionsof Lyapunov-Krasovski and the Fractional Order PID controllaw. The analytical results are illustrated by the simulation offractional nonlinear systems interconnected with time delaywhich are forced to follow complex trajectories as chaoticsystems.Fractional complex dynamical systems, trajectory track-ing, Fractional Order Lyapunov-Krasovskii theory, FractionalOrder PID control law.