通过领导者选择最小化多智能体系统中的收敛误差：一种超模优化方法
Minimizing Convergence Error in Multi-Agent Systems via Leader Selection: A Supermodular Optimization Approach
AI总结：
本文研究多智能体系统中领导者选择问题，通过超模优化方法最小化跟随者智能体的收敛误差，提出两种领导者选择问题并设计算法以处理静态、动态网络。
摘要：
在领导者-跟随者多智能体系统中，领导者作为控制输入影响跟随者状态。跟随者收敛速度及收敛前的误差由领导者选择决定。本文研究领导者选择以最小化跟随者收敛误差，定义为跟随者中间状态与领导者状态凸包的距离范数。通过引入随机游走网络图的新连接，证明收敛误差具有超模结构。超模性使开发高效离散优化算法成为可能，可直接近似最优领导者集合，提供可证明的性能保证，且不依赖连续松弛。在超模优化框架内，提出两种领导者选择问题：固定数量领导者以最小化收敛误差，以及最小集合领导者以达到给定的收敛误差界。在静态、动态已知拓扑分布和动态未知拓扑分布网络中设计算法。数值研究表明，本文方法比现有随机和度数基于的领导者选择方法具有显著更低的收敛误差。
英文摘要：
In a leader-follower multi-agent system (MAS), the leader agents act as control inputs and influence the states of the remaining follower agents. The rate at which the follower agents converge to their desired states, as well as the errors in the follower agent states prior to convergence, are determined by the choice of leader agents. In this paper, we study leader selection in order to minimize convergence errors experienced by the follower agents, which we define as a norm of the distance between the follower agents' intermediate states and the convex hull of the leader agent states. By introducing a novel connection to random walks on the network graph, we show that the convergence error has an inherent supermodular structure as a function of the leader set. Supermodularity enables development of efficient discrete optimization algorithms that directly approximate the optimal leader set, provide provable performance guarantees, and do not rely on continuous relaxations. We formulate two leader selection problems within the supermodular optimization framework, namely, the problem of selecting a fixed number of leader agents in order to minimize the convergence error, as well as the problem of selecting the minimum-size set of leader agents to achieve a given bound on the convergence error. We introduce algorithms for approximating the optimal solution to both problems in static networks, dynamic networks with known topology distributions, and dynamic networks with unknown and unpredictable topology distributions. Our approach is shown to provide significantly lower convergence errors than existing random and degree-based leader selection methods in a numerical study.
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