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Delayed Consensus Problem for Single and Double Integrator Systems

机译：单和双积分器系统的延迟共识问题

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摘要

This work deals with the analysis of the consensus problem for networks of agents constituted by single and double integrator systems. It is assumed that the communication among agents is affected by a constant time-delay. Previous and numerous analysis of the problem shows that the maximum communication time-delay that can be introduced to the network without affecting the consensus of the group of the agents depends on the considered topology. In this work, a control scheme that is based on the estimation of future states of the agents and that allows increasing the magnitude of a possible time-delay affecting the communication channels is proposed. How the proposed delay compensation strategy is independent of the network topology in the sense that the maximum allowable time-delay that could be supported by the network depends on a design parameter and not on the maximum eigenvalue of the corresponding Laplacian matrix is shown. It is formally proven that, under the proposed prediction scheme, the consensus of the group can be achieved by improving the maximum time-delay bounds previously reported in the literature. Numerical simulations show the effectiveness of the proposed solution.
机译：这项工作涉及对由单集成商系统和双集成商系统组成的代理商网络的共识问题的分析。假定代理之间的通信受到恒定时间延迟的影响。对该问题的先前分析和大量分析表明，可以引入网络的最大通信时延而不会影响代理组的共识，这取决于所考虑的拓扑。在这项工作中，提出了一种控制方案，该方案基于对代理的未来状态的估计，并允许增加影响通信信道的可能时间延迟的幅度。从网络可以支持的最大允许时间延迟取决于设计参数，而不取决于相应的拉普拉斯矩阵的最大特征值的意义上，所提出的延迟补偿策略如何独立于网络拓扑。正式证明，在提出的预测方案下，可以通过改善文献中先前报道的最大时延界限来达到小组的共识。数值仿真表明了所提出解决方案的有效性。

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