Zhipeng Liu, Yao Long, Andrew Clark, Phillip Lee, Linda Bushnell, Daniel Kirschen, Radha Poovendran
备注：
This is a revised version of the paper that appeared in the proceedings of the 56th IEEE Conference on Decision and Control (CDC), Melbourne, Australia, December, 2017
This paper studies the problem of selecting a minimum-size set of input nodes to guarantee stability of a networked system in the presence of uncertainties and time delays. Current approaches to input selection in networked dynamical systems focus on nominal systems with known parameter values in the absence of delays. We derive sufficient conditions for existence of a stabilizing controller for an uncertain system that are based on a subset of system modes lying within the controllability subspace induced by the set of inputs. We then formulate the minimum input selection problem and prove that it is equivalent to a discrete optimization problem with bounded submodularity ratio, leading to polynomial-time algorithms with provable optimality bounds. We show that our approach is applicable to different types of uncertainties, including additive and multiplicative uncertainties in the system matrices as well as uncertain time delays. We demonstrate our approach in a numerical case study on the IEEE 39-bus test power system.
Online Learning to Transport via the Minimal Selection Principle
University of Chicago（芝加哥大学）；University of British Columbia（不列颠哥伦比亚大学）
基于运筹学中的鲁棒动态资源分配问题，本文研究了决策变量为概率测度的无穷维对象的\textit{Online Learning to Transport}（OLT）问题。我们通过一种称为最小选择原理的见解，在在线学习、最优运输和偏微分方程之间建立联系，该原理最初由\citet{Ambrosio_2005}在Wasserstein梯度流设置中研究。这使我们能够将标准的在线学习框架无缝地扩展到无限维环境。基于我们的框架，我们推导出一种新的方法，称为\textit{minimal selection or exploration (MSoE) algorithm}解决OLT问题，使用平均场近似和离散化技术。在位移凸设置，支撑我们的方法的主要理论信息是，随着时间的推移，最小化运输成本（通过最小选择原则），确保最佳的累积遗憾上限。在算法方面，我们的MSoE算法适用于位移凸设置之外，使得最优传输的数学理论实际上与动态资源分配中常见的非凸设置相关。
Portfolio Selection by Joint Estimation-Robustness Optimization with the Return and Risk Constraints
Academy for Advanced Interdisciplinary Studies, Peking University（北京大学前沿交叉学科研究院）；School of Mathematics and Statistics, Beijing Jiaotong University（北京交通大学数学与统计学院）；School of Mathematical Sciences, University of Southampton（南安普顿大学数学科学学院）；Department of Data Science and Artificial Intelligence, The Hong Kong Polytechnic University（香港理工大学数据科学与人工智能系）
A dimension reduction procedure for the selection of Two-spring lattice-spring topologies with minimal fabrication cost and required weighted force-resistance performance
