Robust Weighted-Average Continuous-Time Consensus With Communication Time Delay
研究了多智能体系统中同时优化一致性算法对时延的鲁棒性和收敛率的问题，将其建模为多目标优化问题，并证明帕累托前沿仅依赖于拉普拉斯矩阵的最优条件数，通过半定规划求解得到最优权重。
Achieving consensus behavior robust to time delay in multiagent systems has attracted much attention. This work is concerned with optimizing the convergence rate of the consensus algorithm in such systems with time delays. Previous approaches optimize either the robustness to time delay or the convergence rate separately, while imposing a limit on the other. Eigenratio optimization is another method, which does not necessarily result in a unique set of weights. Here, the problem is treated in its general form as a multiobjective optimization problem. It is shown that the corresponding Pareto frontier depends solely on the optimal condition number of the Laplacian, and it includes the optimal answer of previously adopted approaches as special cases. A notion of optimal consensusability is then defined, which allows a particular point on the Pareto Frontier with special properties to be identified. The resulting optimization problem is shown to be convex, as is solved by reformulating it as a standard semidefinite programming problem. The optimal weights for individual topologies, clique lifted graphs, and different types of subgraphs are provided, where for the latter, the optimal weights have shown to be independent of the rest of topology. Through numerical simulations, the tradeoff between robustness and convergence rate is demonstrated.