In this paper, we investigate the cooperative control problem of high-order integrators under heterogeneous couplings. A new class of distributed control algorithms are developed for the designated convergence rate (DCR) problem of high-order integrators, which could explicitly show the convergence margin of the closed-loop system, and has better robustness than conventional consensus algorithms. We first propose state consensus control algorithms for high-order integrators, where necessary and sufficient convergence conditions are proposed by theoretical analysis. Then we extend the results to the case of output leaderless consensus of heterogeneous high-order integrators with heterogeneous couplings. Finally, simulation examples are given to validate the effectiveness of the proposed algorithms.

在本文中，我们研究了异构耦合下高阶积分器的协同控制问题。针对高阶积分器的指定收敛率（DCR）问题，开发了一类新的分布式控制算法，该算法可以明确地显示闭环系统的收敛裕度，并且比传统的一致性算法具有更好的鲁棒性。我们首先提出了高阶积分器的状态一致性控制算法，其中通过理论分析提出了必要和充分的收敛条件。然后我们将结果扩展到具有异构耦合的异构高阶积分器的输出无领导共识的情况。最后通过仿真实例验证了所提算法的有效性。