继续使用非侵入性控制方案：揭示行人疏散场景中的不稳定状态
Continuation with Non-invasive Control Schemes: Revealing Unstable States in a Pedestrian Evacuation Scenario
摘要：
本文提出了一个框架，在实验室实验或模拟进行分叉分析。我们采用控制为基础的延续，研究微观定义的模型的宏观变量的动态，探索潜在的可行性的基础反馈控制技术在实验中。在以前的实验研究中，使用迭代根查找方法的反馈控制目标，我们提出了一个反馈控制律，本质上是非侵入性的。也就是说，控制发现平衡的位置，并同时稳定它们。我们称之为零平衡反馈控制，我们证明了它是能够稳定的平衡分支，除了在余维n+1，其中n是状态空间维度的反馈可以dependenton.We应用该方法模拟疏散的情况下，行人必须到达一个出口后，操纵左或右周围的障碍物的奇异性。在微观模拟中，该方案显示了两种可能的稳定行人流之间的双稳态和倾斜的滞后现象。我们证明了疏散的情况下，所提出的控制律是能够均匀地发现和稳定沿整个分支的稳定流，包括点，其他非侵入性的方法，反馈控制变得奇异。
英文摘要：
This paper presents a framework to perform bifurcation analysis in laboratory experiments or simulations. We employ control-based continuation to study the dynamics of a macroscopic variable of a microscopically defined model, exploring the potential viability of the underlying feedback control techniques in an experiment. In contrast to previous experimental studies that used iterative root-finding methods on the feedback control targets, we propose a feedback control law that is inherently non-invasive. That is, the control discovers the location of equilibria and stabilizes them simultaneously. We call the proposed control zero-in-equilibrium feedback control and we prove that it is able to stabilize branches of equilibria, except at singularities of codimension n+1, where n is the number of state space dimensions the feedback can depend on. We apply the method to a simulated evacuation scenario were pedestrians have to reach an exit after maneuvering left or right around an obstacle. The scenario shows a hysteresis phenomenon with bistability and tipping between two possible steady pedestrian flows in microscopic simulations. We demonstrate for the evacuation scenario that the proposed control law is able to uniformly discover and stabilize steady flows along the entire branch, including points where other non-invasive approaches to feedback control become singular.
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