基于集合信心的意见动态:收敛标准和周期性解决方案

IF 2.4 Q2 AUTOMATION & CONTROL SYSTEMS IEEE Control Systems Letters Pub Date : 2024-10-14 DOI:10.1109/LCSYS.2024.3479275
Iryna Zabarianska;Anton V. Proskurnikov
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引用次数: 0

摘要

这封信介绍了海格塞曼-克劳斯(Hegselmann-Krause,HK)意见动态模型的一个新的多维扩展,在这个模型中,意见接近度不是由规范或度量决定的。取而代之的是,每个代理信任闵科夫斯基总和 $\boldsymbol {\xi }+\boldsymbol {\mathcal {O}}$ 内的意见,其中 $\boldsymbol {\xi }$ 是代理当前的意见,$\boldsymbol {\mathcal {O}}$ 是定义可接受偏差的置信度集。在每次迭代过程中,代理通过同时平均可信意见来更新自己的意见。在传统的香港系统中,$\boldsymbol {\mathcal {O}}$ 是一个符合某种规范的球,而我们的模型则不同,它允许置信度集是非凸的,甚至是无界的。这种新模型被称为 SCOD(基于置信度的意见动态模型),它可以表现出传统 HK 模型所不具备的特性。一些解可能会收敛到状态空间中的非平衡点,而另一些解则会周期性振荡。如果集合$\boldsymbol {\mathcal {O}}$是对称的,并且其内部包含零,那么这些 "病态 "就会消失:与通常的HK模型类似,SCOD会在有限次数的迭代中收敛到其中一个平衡点。如果一个代理是 "顽固的",不愿意改变自己的观点,但仍会影响其他代理,那么后一个属性也会保留;但是,两个顽固的代理会导致振荡。
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Opinion Dynamics With Set-Based Confidence: Convergence Criteria and Periodic Solutions
This letter introduces a new multidimensional extension of the Hegselmann-Krause (HK) opinion dynamics model, where opinion proximity is not determined by a norm or metric. Instead, each agent trusts opinions within the Minkowski sum $\boldsymbol {\xi }+\boldsymbol {\mathcal {O}}$ , where $\boldsymbol {\xi }$ is the agent’s current opinion and $\boldsymbol {\mathcal {O}}$ is the confidence set defining acceptable deviations. During each iteration, agents update their opinions by simultaneously averaging the trusted opinions. Unlike traditional HK systems, where $\boldsymbol {\mathcal {O}}$ is a ball in some norm, our model allows the confidence set to be non-convex and even unbounded. The new model, referred to as SCOD (Set-based Confidence Opinion Dynamics), can exhibit properties absent in the conventional HK model. Some solutions may converge to non-equilibrium points in the state space, while others oscillate periodically. These “pathologies” disappear if the set $\boldsymbol {\mathcal {O}}$ is symmetric and contains zero in its interior: similar to the usual HK model, the SCOD then converge in a finite number of iterations to one of the equilibrium points. The latter property is also preserved if one agent is “stubborn” and resists changing their opinion, yet still influences the others; however, two stubborn agents can lead to oscillations.
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来源期刊
IEEE Control Systems Letters
IEEE Control Systems Letters Mathematics-Control and Optimization
CiteScore
4.40
自引率
13.30%
发文量
471
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