We define the complexity of a continuous-time linear system to be the minimum number of bits required to describe its forward increments to a desired level of fidelity, and compute this quantity using the rate distortion function of a Gaussian source of uncertainty in those increments. The complexity of a linear system has relevance in control-communications contexts requiring local and dynamic decision-making based on sampled data representations. We relate this notion of complexity to the design of attention-varying controllers, and demonstrate a novel methodology for constructing source codes via the endpoint maps of so-called emulating systems, with potential for non-parametric, data-based simulation and analysis of unknown dynamical systems.

翻译：我们定义连续时间线性系统的复杂度为描述其前向增量至期望保真度所需的最小比特数，并通过刻画这些增量中高斯不确定性源的率失真函数计算该度量。线性系统的复杂度在需要基于采样数据表征进行局部动态决策的控制-通信场景中具有重要相关性。我们将该复杂度概念与注意力变化型控制器设计相关联，并展示一种通过所谓模拟系统的端点映射构建信源编码的新颖方法论，该方法有望用于未知动力系统的非参数化数据驱动仿真与分析。