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

This paper presents an extension to the theory on the analysis of stability of complex systems with time delay of fractional order, the previous study is based on the theory of functions of Lyapunov-Krasovski and the Fractional Order PID control law. The analytical results are illustrated by the simulation of fractional nonlinear systems interconnected with time delay which are forced to follow complex trajectories as chaotic systems.Fractional complex dynamical systems, trajectory tracking, Fractional Order Lyapunov-Krasovskii theory, Fractional Order PID control law.