The paper deals with the distributed minimum sharing problem: a set of decision-makers compute the minimum of some local quantities of interest in a distributed and decentralized way by exchanging information through a communication network. We propose an adjustable approximate solution which enjoys several properties of crucial importance in applications. In particular, the proposed solution has good decentralization properties and it is scalable in that the number of local variables does not grow with the size or topology of the communication network. Moreover, a global and uniform (both in the initial time and in the initial conditions) asymptotic stability result is provided towards a steady state which can be made arbitrarily close to the sought minimum. Exact asymptotic convergence can be recovered at the price of losing uniformity with respect to the initial time.

该论文涉及分布式最小共享问题：一组决策者通过通信网络交换信息，以分布式和分散的方式计算一些局部感兴趣量的最小值。我们提出了一个可调整的近似解，它在应用中具有几个至关重要的特性。特别是，所提出的解决方案具有良好的分散特性，并且它是可扩展的，因为局部变量的数量不会随着通信网络的大小或拓扑结构而增长。此外，全局和均匀（在初始时间和初始条件下）渐近稳定性结果被提供给稳定状态，该稳定状态可以任意接近所寻求的最小值。