By applying the fractional Lyapunov direct method, we investigate the robust consensus tracking problem for a class of uncertain fractional-order multiagent systems with a leader whose input is unknown and bounded. More specifically, multiple fractional-order systems with heterogeneous unknown nonlinearities and external disturbances are considered in this paper, which include the second-order multiagent systems as its special cases. First, a discontinuous neural network-based (NN-based) distributed robust adaptive algorithm is designed to guarantee the consensus tracking error exponentially converges to zero under a fixed topology. Also the derived results are further extended to the case of switching topology by appropriately choosing multiple Lyapunov functions. Second, a continuous NN-based distributed robust adaptive algorithm is further proposed to eliminate the undesirable chattering phenomenon of the discontinuous controller, where the consensus tacking error is uniformly ultimately bounded and can be reduced as small as desired. It is worth noting that all the proposed NN-based robust adaptive algorithms are independent of any global information and thus are fully distributed. Finally, numerical simulations are provided to validate the correctness of the proposed algorithms.

In this study, Mittag–Leffler stability and the fractional Lyapunov direct method are used to study fractional‐order leaderless and leader‐following consensus algorithms with non‐linear dynamics under a directed network topology. The sufficient conditions are given to guarantee that the consensus can be achieved in the non‐linear fractional‐order systems with and without a virtual leader, and the adaptive feedback control protocols are also given in this study. Finally, some numerical simulations are presented to demonstrate the effectiveness of the theoretical results.

This paper addresses the problem of distributed fixed-time optimization for heterogeneous second-order nonlinear multiagent systems with local time-varying cost functions. The objective is to cooperatively minimize a convex global time-varying cost function formed by a sum of local time-varying cost functions in a fixed time, where each local cost function is not necessarily required to be convex. A state feedback distributed fixed-time optimization controller with an estimator-based distributed optimization term is first presented. In order to overcome the lack of the absolute velocity measurements, a distributed fixed-time observer is designed to estimate the absolute velocity information of each agent. Based on the designed observer, a novel output feedback distributed fixed-time optimization controller using only local output measurements is further presented. Both of the presented state and output feedback distributed fixed-time optimization controllers ensure that all agents reach a consensus while minimizing the global cost function within a fixed time. The restrictive bound of the fixed time is estimated explicitly, which is irrelevant to any initial conditions. Finally, a numerical simulation is provided to validate the results.