Wang Peijun, Wen Guanghui, Huang Tingwen, Yu Wenwu, Ren Yong
IEEE Trans Cybern. 2022 Jan;52(1):630-640. doi: 10.1109/TCYB.2020.2981518. Epub 2022 Jan 11.
We aim to address the consensus tracking problem for multiple-input-multiple-output (MIMO) linear networked systems under directed switching topologies, where the leader is subject to some nonzero but norm bounded inputs. First, based on the relative outputs, a full-order unknown input observer (UIO) is designed for each agent to track the full states' error among neighboring agents. With the aid of such an observer, a discontinuous feedback protocol is subtly designed. And it is proven that consensus tracking can be achieved in the closed-loop networked system if the average dwell time (ADT) for switching among different interaction graph candidates is larger than a given positive threshold. By using the boundary layer technique, a continuous feedback protocol is skillfully designed and employed. It is shown that the consensus error converges into a bounded set under the designed continuous protocol. Second, as part of the full states' error can be constructed via the agents' outputs, a reduced-order UIO is thus designed based on which discontinuous and continuous feedback protocols are, respectively, proposed. By using the stability theory of the switched systems, it is proven that the consensus error converges asymptotically to 0 under the designed discontinuous protocol, and converges into a bounded set under the designed continuous protocol. Finally, the obtained theoretical results are validated through simulations.
我们旨在解决有向切换拓扑下多输入多输出（MIMO）线性网络系统的一致性跟踪问题，其中领导者受到一些非零但范数有界的输入。首先，基于相对输出，为每个智能体设计一个全阶未知输入观测器（UIO），以跟踪相邻智能体之间全状态的误差。借助这样一个观测器，巧妙地设计了一种不连续反馈协议。并且证明了，如果在不同交互图候选之间切换的平均驻留时间（ADT）大于给定的正阈值，则闭环网络系统中可以实现一致性跟踪。通过使用边界层技术，巧妙地设计并采用了一种连续反馈协议。结果表明，在设计的连续协议下，一致性误差收敛到一个有界集。其次，由于全状态误差的一部分可以通过智能体的输出构造，因此设计了一个降阶UIO，并在此基础上分别提出了不连续和连续反馈协议。利用切换系统的稳定性理论，证明了在设计的不连续协议下，一致性误差渐近收敛到0，而在设计的连续协议下，一致性误差收敛到一个有界集。最后，通过仿真验证了所得到的理论结果。
