时变仿射意见网络的稀疏一步超前最优控制：跟踪与竞争博弈
Sparse One-Step-Ahead Optimal Control of Time-Varying Affine Opinion Networks: Tracking and Competitive Games
- Federal University of Rio de Janeiro（里约热内卢联邦大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文针对时变仿射意见网络，提出一种稀疏一步超前最优控制方法，通过排序实现精确支持选择，并扩展到竞争博弈场景，验证了跟踪性能与均衡存在性。
AI中文摘要：
本文研究时变意见网络中资源受限的外部影响问题，此时控制器必须在每次更新时同时选择一小部分智能体和一个标量干预。我们采用仿射自由响应（包括DeGroot和Friedkin-Johnsen动力学），随后进行直接稀疏作用。消除标量作用将一步问题简化为基数受限的支持集目标，其全局最优解由最大或最小残差分量获得。因此，精确的稀疏一步超前最优控制只需一次排序和O(|T|log|T|)次操作，其中T为支持集。对于周期仿射动力学，所得的状态相关低秩反馈允许基于周期的终极界和对模型不变目标的精确跟踪。DeGroot和Friedkin-Johnsen特例揭示了目标不变性和仿射失配项的作用。当存在多个竞争外部参与者时，每个稀疏最优响应保持相同的排序结构，完整的二元-连续阶段博弈是精确势博弈，因此在每个冻结状态都存在纯策略均衡。同状态福利基准将标量竞争造成的损失与战略支持选择造成的额外损失分开。数值示例验证了精确支持选择，并说明了切换顺序效应、DeGroot/Friedkin-Johnsen跟踪、资源权衡和竞争实现。
英文摘要：
This paper studies resource-limited external influence in time-varying opinion networks when a controller must choose both a small set of agents and a scalar intervention at each update. We use the affine free response, which includes DeGroot and Friedkin--Johnsen dynamics, followed by a direct sparse action. Eliminating the scalar action reduces the one-step problem to a cardinality-constrained support objective whose global optimum is obtained from the largest or smallest residual components. Hence exact sparse one-step-ahead optimal control requires one sort and \(O(|\mathcal T|\log|\mathcal T|)\) operations, where \(\mathcal T\) is the support set. For periodic affine dynamics, the resulting state-dependent low-rank feedback admits cycle-based ultimate bounds and exact tracking of model-invariant targets. The DeGroot and Friedkin--Johnsen specializations expose the role of target invariance and the affine mismatch term. With several competing external players, each sparse best response retains the same sorting structure and the complete binary--continuous stage game is an exact potential game, so a pure-strategy equilibrium exists at every frozen state. Same-state welfare benchmarks separate loss due to scalar competition from the additional loss due to strategic support selection. Numerical examples validate exact support selection and illustrate switching-order effects, DeGroot/Friedkin--Johnsen tracking, resource tradeoffs, and competitive implementations.
