Distributed Coordination of Fractional Dynamical Systems with Exogenous Disturbances

Abstract

Distributed coordination of fractional multiagent systems with external disturbances is studied. The state observer of fractional dynamical system is presented, and an adaptive pinning controller is designed for a little part of agents in multiagent systems without disturbances. This adaptive pinning controller with the state observer can ensure multiple agents' states reaching an expected reference tracking. Based on disturbance observers, the controllers are composited with the pinning controller and the state observer. By applying the stability theory of fractional order dynamical systems, the distributed coordination of fractional multiagent systems with external disturbances can be reached asymptotically.

Neural Networks Based Adaptive Consensus for a Class of Fractional‐Order Uncertain Nonlinear Multiagent Systems

“…Remark 7. Different from the results in [27][28][29][30][31], where the Lipschitz condition and the boundedness condition are demanded to achieve consensus of fractional-order MASs, the results in this paper do not include above rigorous conditions, and they provide a control method to solve the consensus problem for the general nonlinear fractional-order MASs.…”

“…In addition, various valid control laws are designed to solve different problems based on different control methods, such as the adaptive control method [22], the fractional-order PID control method [23], the sliding mode control method [24], and the event triggering control method [25]. Moreover, MASs have been studied from the linear systems to the nonlinear systems [26][27][28][29][30][31], where researchers have focused on studying the nonlinear fractional-order MASs; they can cause systems degraded performance or instability, and they are both inevitable in practical applications for the dynamic systems or the effectiveness of the external disturbance; therefore, it is necessary to consider the nonlinear MASs.…”

“…Meanwhile, the limitations for the nonlinear term and the external disturbance term can be reduced. Up to now, some results [28,32] have designed the observer-type control law to avoid obtaining the unknown information in fractional-order MASs, but most of them discuss the linear MASs.…”

“…Compared to the existing results on fractionalorder MASs, this paper mainly has the following differences. Firstly, compared with the results about the fractional-order nonlinear MASs [27][28][29][30][31], this paper discusses the general fractional-order nonlinear MASs with external disturbance, where the Lipschitz condition and boundedness condition are not necessary for the nonlinear terms. Secondly, different from the existing control methods [22][23][24][25], the paper designs a developed RBFNNs based approximation control law to overcome the unknown nonlinear terms in fractional-order MASs.…”