Fractional Complex Dynamical Systems for Trajectory Tracking using Fractional Neural Network via Fractional Order PID Control Law

In this paper the problem of trajectory tracking is studied.Based on the Lyapunov theory, a Fractional Order PIDcontrol lawthat achieves the global asymptotic stability of the trackingerror between a fractional order recurrent neural network anda fractional order complex dynamical network is obtained. Toillustrate the analytic results we present a tracking simulationof a dynamical network with each node being just one frac-tional order Lorenz´ s dynamical system and three identicalfractional order Chen’s dynamical systems.