Gong Ping, Han Qing-Long, Lan Weiyao
IEEE Trans Cybern. 2022 Jan;52(1):65-76. doi: 10.1109/TCYB.2020.2977169. Epub 2022 Jan 11.
This article investigates the problem of finite-time consensus tracking for incommensurate fractional-order nonlinear multiagent systems (MASs) with general directed switching topology. For the leader with bounded but arbitrary dynamics, a neighborhood-based saturated observer is first designed to guarantee that the observer's state converges to the leader's state in finite time. By utilizing a fuzzy-logic system to approximate the heterogeneous and unmodeled nonlinear dynamics, an observer-based adaptive parameter control protocol is designed to solve the problem of finite-time consensus tracking of incommensurate fractional-order nonlinear MASs on directed switching topology with a restricted dwell time. Then, the derived result is further extended to the case of directed switching topology without a restricted dwell time by designing an observer-based adaptive gain control protocol. By artfully choosing a piecewise Lyapunov function, it is shown that the consensus tracking error converges to a small adjustable residual set in finite time for both the cases with and without a restricted dwell time. It should be noted that the proposed adaptive gain consensus tracking protocol is completely distributed in the sense that there is no need for any global information. The effectiveness of the proposed consensus tracking scheme is illustrated by numerical simulations.
本文研究具有一般有向切换拓扑的非 commensurate 分数阶非线性多智能体系统（MASs）的有限时间一致性跟踪问题。对于具有有界但任意动力学的领导者，首先设计了一种基于邻域的饱和观测器，以保证观测器状态在有限时间内收敛到领导者状态。通过利用模糊逻辑系统逼近异构和未建模的非线性动力学，设计了一种基于观测器的自适应参数控制协议，以解决具有受限驻留时间的有向切换拓扑上非 commensurate 分数阶非线性 MASs 的有限时间一致性跟踪问题。然后，通过设计一种基于观测器的自适应增益控制协议，将所得结果进一步扩展到无受限驻留时间的有向切换拓扑情况。通过巧妙选择分段 Lyapunov 函数，结果表明，对于有受限驻留时间和无受限驻留时间的两种情况，一致性跟踪误差在有限时间内收敛到一个小的可调节残差集。需要注意的是，所提出的自适应增益一致性跟踪协议在不需要任何全局信息的意义上是完全分布式的。数值仿真验证了所提出的一致性跟踪方案的有效性。
