Observability Variation in Emergent Dynamics: A Study using Krylov Subspace-based Model Order Reduction
Observability Variation in Emergent Dynamics: A Study using Krylov Subspace-based Model Order Reduction
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DOI：
10.23919/acc45564.2020.9147750
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发表时间：
2020-07
期刊：
影响因子：
--
通讯作者：
Zhaohui Yang;Kshitij Jerath
中科院分区：
文献类型：
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作者：
Zhaohui Yang;Kshitij Jerath
大规模自组织系统通常表现出紧急行为，表现为低维流形上的降阶动力学，其维数远小于原始状态空间。以有意义的方式影响这种自组织系统的能力依赖于观察由此产生的紧急行为。虽然先前的研究从多智能体系统的网络结构和连通性的角度考察了与可观察性相关的概念，但对宏观尺度的可观察性（即观察自组织系统的降阶状态的能力）的认识有限。在这项工作中，研究了复杂系统中感知或观察紧急行为的能力，并提出了可观察性度量与模型阶数之间的关系。基于Krylov子空间的方法已被用于执行非线性系统的模型阶约简，如耦合Rössler系统和具有低流形紧急行为的互连电路。数值模拟结果表明，作为紧急现象代表的降阶模型通常具有较高的可观测性指标。
Large-scale self-organizing systems often exhibit emergent behaviors which manifest as reduced-order dynamics on a low-dimensional manifold with a dimension much smaller than that of the original state-space. The ability to influence such self-organizing systems in a meaningful manner relies on observing the resulting emergent behaviors. While prior research has examined observability-related concepts from the viewpoint of network structure and connectivity in multiagent system, there exist limited insights into macroscopic-scale observability, i.e. the ability to observe reduced-order states of self-organizing systems. In this work, the ability to perceive or observe emergent behaviors in complex systems has been studied, and the relationship between an observability metric and model orders has been presented. Krylov subspace-based methods have been used to perform model order reduction for nonlinear systems such as coupled Rössler systems and interconnected electrical circuits that exhibit low-manifold emergent behaviors. The resulting numerical simulations indicate that reduced-order models, which are representative of emergent phenomena, usually possess higher observability metrics.