Motivated by control with communication constraints, in this work we develop a time-invariant data compression architecture for linear-quadratic-Gaussian (LQG) control with minimum bitrate prefix-free feedback. For any fixed control performance, the approach we propose nearly achieves known directed information (DI) lower bounds on the time-average expected codeword length. We refine the analysis of a classical achievability approach, which required quantized plant measurements to be encoded via a time-varying lossless source code. We prove that the sequence of random variables describing the quantizations has a limiting distribution and that the quantizations may be encoded with a fixed source code optimized for this distribution without added time-asymptotic redundancy. Our result follows from analyzing the long-term stochastic behavior of the system, and permits us to additionally guarantee that the time-average codeword length (as opposed to expected length) is almost surely within a few bits of the minimum DI. To our knowledge, this time-invariant achievability result is the first in the literature.
翻译:基于对通信限制的控制,在这项工作中,我们为线性赤道-Gausian(LQG)控制开发了一个时间变化数据压缩结构,使用最少的比特率前缀反馈。对于任何固定的控制性工作,我们建议的方法几乎能够达到已知的定向信息(DI)在时间平均预期编码长度上较低的界限。我们改进了对古典可实现性方法的分析,该方法要求通过时间变化的无损源代码对工厂测量进行量化编码。我们证明,描述定量的随机变量序列分布有限,而且量化可能以固定源码编码编码,为这种分布优化,而没有增加时间障碍冗余。我们的结果是分析系统的长期随机行为,并允许我们进一步保证,时间平均编码长度(相对于预期长度)几乎肯定在最小的DI的几位内。据我们所知,这种时间可变性是文献中的第一个结果。