用于建模初级视觉皮层$V1$的4维可解李群上的线性控制系统
Linear control systems on a 4D solvable Lie group used to model primary visual cortex $V1$
AI总结：
本文研究4维可解李群上的线性控制系统，采用$G(\omega)=\mathbb{R}^{2}\times S^{1}\times S^{1}$作为状态空间群建模初级视觉皮层$V1$，并给出了能控性新结果及控制集的刻画。
摘要：
本文研究4维可解李群上的线性控制系统。我们的动机源于\cite{baspinar}中引入的模型，该模型提出了一个精确的几何框架，将初级视觉皮层$V1$解释为视网膜平面$M$（等同于$\mathbb{R}^{2}$）上的纤维丛，以方向$θ\in S^{1}$、空间频率$ω\in \mathbb{R}^{+}$和相位$ϕ\in S^{1}$作为内在参数。对于每个固定频率$ω$，该模型定义了李群$G(ω) = \mathbb{R}^{2} \times S^{1} \times S^{1}$，我们在本工作中将其作为线性控制系统的状态空间群$G$。我们还提出了关于能控性的新结果，并刻画了与该类系统相关的控制集。
英文摘要：
In this article, we study linear control systems on a 4-dimensional solvable Lie group. Our motivation stems from the model introduced in \cite{baspinar}, which presents a precise geometric framework in which the primary visual cortex $V1$ is interpreted as a fiber bundle over the retinal plane $M$ (identified with $\mathbb{R}^{2}$), with orientation $θ\in S^{1}$, spatial frequency $ω\in \mathbb{R}^{+}$, and phase $ϕ\in S^{1}$ as intrinsic parameters. For each fixed frequency $ω$, this model defines a Lie group $G(ω) = \mathbb{R}^{2} \times S^{1} \times S^{1}$, which we adopt in this work as the state space group $G$ of our linear control system. We also present new results concerning controllability and characterize the control sets associated with this class of systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
