The application of the fast sliding-mode control technique on solving consensus problems of fractional-order multiagent systems is investigated. The design and analysis are based on a combination of the distributed coordination theory and the knowledge of fractional-order dynamics. First, a sliding-mode manifold (surface) vector is defined, and then the fractional-order multiagent system is transformed into an integer-order (namely, first-order) multiagent system. Second, based on the fast sliding-mode control technique, a protocol is proposed for the obtained first-order multiagent system. Third, a new Lyapunov function is presented. By suitably estimating the derivative of the Lyapunov function, the reachability of the sliding-mode manifold is derived. It is proved that the exponential finite-time consensus can be achieved if the communication network has a directed spanning tree. Finally, the effectiveness of the proposed algorithms is demonstrated by some examples.

中文翻译：

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分数阶多智能体系统的指数有限时间共识

研究了快速滑模控制技术在解决分数阶多智能体系统一致性问题中的应用。设计和分析基于分布式协调理论和分数阶动力学知识的结合。首先定义一个滑模流形（表面）向量，然后将分数阶多智能体系统转化为整数阶（即一阶）多智能体系统。其次，基于快速滑模控制技术，为获得的一阶多智能体系统提出了一种协议。第三，提出了一个新的李雅普诺夫函数。通过适当地估计李雅普诺夫函数的导数，可以推导出滑模流形的可达性。证明如果通信网络具有有向生成树，则可以实现指数有限时间共识。最后，通过一些例子证明了所提出算法的有效性。