On the complexity of linear systems: an approach via rate distortion theory and emulating systems

Eric Wendel; John Baillieul; Joseph Hollmann

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arXiv · 2306.02435

On the complexity of linear systems: an approach via rate distortion theory and emulating systems

Eric Wendel·John Baillieul·Joseph Hollmann

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Abstract

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.

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Eric Wendel, John Baillieul, Joseph Hollmann. 2023-06-04. On the complexity of linear systems: an approach via rate distortion theory and emulating systems. https://arxiv.org/abs/2306.02435

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