Minimum Rate For Partially Observable Linear System with Side Information: LQG Plant and Gaussian-Markov Source

2026-08-27

AI Summary

本文研究了具有侧信息的部分可观线性系统的最小所需速率问题，使用LQG模型和高斯-马尔可夫源，通过一类线性策略优化条件定向信息下界。

Abstract

This paper studies the minimum rate required for a partially observable linear system with side information. The Linear Quadratic Gaussian(LQG) plant and the Gaussian-Markov source are considered. We show that a class of linear policies is sufficient for optimizing the conditional directed information lower bound. We also show that the resulting optimization problem is convex for the scalar case in both time-varying and time-invariant systems. Our results generalize the past works that consider the case with full or partial observation only, and the case with full observation and side information. Numerical simulations are presented to illustrate the effect of side information for partially observable systems.

Problem

• partially observable linear system
• side information
• minimum rate
• LQG plant
• Gaussian-Markov source

Innovation

• linear policies
• conditional directed information
• convex optimization
• partially observable systems
• side information