Dynamic Event-Triggered Control for a Class of Nonlinear Fractional-Order Systems

In this brief, we contribute to adaptive neural network (NN) backstepping control design for the nonlinear double-integrator fractional-order (FO) systems comprising unknown dynamics and disturbances by the event-triggered procedure. To this end, a new triggering rule with a dynamical variable is first introduced, including some available static triggering rules as its particular form. Then, by using the contradiction and some properties of the Mittag-Leffler function, it is proved for the first time that the applied dynamical variable is positive and bounded for the FO systems. Hence, the inter-event time between any two successive triggering moments can be enlarged than static event-triggered results. By integrating the backstepping approach into the NN, an adaptive NN controller is constructed, which introduces a new analysis viewpoint on the Zeno phenomenon avoidance for the FO controllers. Under this controller, the tracking error converges to a small compact set including the origin. Finally, an example is given to show the feasibility of the proposed method.

Automated summary

This paper introduces a design of adaptive neural network backstopping control for nonlinear double-integrator fractional-order systems using an event-triggered program. By introducing a new triggering rule and combining the properties of the Mittag-Leffler function, it is proven that the applied dynamic variable is positive and bounded for the systems, allowing for larger event intervals than static triggering rules. By integrating the backstepping method with NN, an adaptive NN controller is constructed to avoid the Zeno phenomenon and ensure convergence of tracking error to a small compact set.