In this work, we study an LQG control system where one of two feedback channels is discrete and incurs a communication cost. We assume that a decoder (co-located with the controller) can make noiseless measurements of a subset of the state vector (referred to as side information) meanwhile a remote encoder (co-located with a sensor) can make arbitrary measurements of the entire state vector, but must convey its measurements to the decoder over a noiseless binary channel. Use of the channel incurs a communication cost, quantified as the time-averaged expected length of prefix-free binary codeword. We study the tradeoff between the communication cost and control performance. The formulation motivates a constrained directed information minimization problem, which can be solved via convex optimization. Using the optimization, we propose a quantizer design and a subsequent achievability result.
翻译:在这项工作中,我们研究一个LQG控制系统,其中两个反馈渠道中的一个是离散的,产生通信成本。我们假设一个解码器(与控制器合用同一地点)可以对状态矢量的一个子子(称为侧信息)进行无噪音的测量,而一个远程编码器(与传感器合用同一地点)则可以任意测量整个状态矢量,但必须将测量结果传递给无噪音二进制信道的解码器。使用该频道将产生通信成本,以不使用前缀二进代码的预期时间长度量化。我们研究通信成本和控制性能之间的平衡。该配方引发一个有限的定向信息最小化问题,可以通过配置优化来解决。我们利用优化,提出一个四分解器设计,并随后提出一个可实现的结果。