Search

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.

This letter presents a distributed solution for consensus control of a network of single-integrator incommensurate fractional-order systems with nonlinear and uncertain dynamics. To consider a broader class of fractional-order systems, compared to existing results, the fractional derivative orders of agents’ dynamics are assumed non-identical, which makes the distributed control design more challenging. To cope with non-identical fractional derivative orders, the Mittag-Leffler function method is adopted to develop a novel distributed control scheme that guarantees consensus under mild assumptions. To deal with agents’ dynamic uncertainties, the proposed approach is integrated with adaptive neural networks to make the distributed tracking errors for all follower agents converge to a small neighborhood of origin. A numerical example is provided to demonstrate the effectiveness of the proposed method.