Distributed Adaptive Cooperative Tracking of Uncertain Nonlinear Fractional-order Multi-agent Systems

In this paper, the leader-following tracking problem of fractional-order multi-agent systems is addressed. The dynamics of each agent may be heterogeneous and has unknown nonlinearities. By assumptions that the interaction topology is undirected and connected and the unknown nonlinear uncertain dynamics can be parameterized by a neural network, an adaptive learning law is proposed to deal with unknown nonlinear dynamics, based on which a kind of cooperative tracking protocols are constructed. The feedback gain matrix is obtained to solve an algebraic Riccati equation. To construct the fully distributed cooperative tracking protocols, the adaptive law is also adopted to adjust the coupling weight. With the developed control laws, we can prove that all signals in the closed-loop systems are guaranteed to be uniformly ultimately bounded. Finally, a simple simulation example is provided to illustrate the established result.