线性多智能体系统中链路噪声下的领导者选择的超模优化框架
A Supermodular Optimization Framework for Leader Selection under Link Noise in Linear Multi-Agent Systems
AI总结：
针对通信链路噪声下线性多智能体系统的稳态均方误差最小化问题，提出基于超模优化的领导者选择方法，并给出可证明的性能界。
摘要：
在多智能体系统（MAS）的许多应用中，一组领导者智能体作为控制输入作用于剩余的跟随者智能体。本文提出了一种分析性的领导者选择方法，以最小化在存在噪声通信链路的情况下，稳态时跟随者智能体状态与其期望值之间的总均方误差。我们证明了选择领导者以最小化该误差的问题可以通过超模优化技术求解，从而得到在可证明的最优界内的高效算法。我们在框架内制定了两个领导者选择问题，即选择固定数量的领导者以最小化误差的问题，以及选择最小数量的领导者以达到可容忍误差水平的问题。我们研究了不同场景下的两种领导者选择准则，包括具有静态拓扑、经历随机链路或节点故障的拓扑、切换拓扑以及由于节点移动而随时间任意变化的拓扑的MAS。除了为所有这些情况提供可证明的界外，仿真结果表明，我们的方法优于其他领导者选择方法（如基于节点度和随机选择的方法），并与当前最先进的算法性能相当。
英文摘要：
In many applications of multi-agent systems (MAS), a set of leader agents acts as a control input to the remaining follower agents. In this paper, we introduce an analytical approach to selecting leader agents in order to minimize the total mean-square error of the follower agent states from their desired value in steady-state in the presence of noisy communication links. We show that the problem of choosing leaders in order to minimize this error can be solved using supermodular optimization techniques, leading to efficient algorithms that are within a provable bound of the optimum. We formulate two leader selection problems within our framework, namely the problem of choosing a fixed number of leaders to minimize the error, as well as the problem of choosing the minimum number of leaders to achieve a tolerated level of error. We study both leader selection criteria for different scenarios, including MAS with static topologies, topologies experiencing random link or node failures, switching topologies, and topologies that vary arbitrarily in time due to node mobility. In addition to providing provable bounds for all these cases, simulation results demonstrate that our approach outperforms other leader selection methods, such as node degree-based and random selection methods, and provides comparable performance to current state of the art algorithms.
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