We propose an adaptive coding approach to achieve linear-quadratic-Gaussian (LQG) control with near-minimum bitrate prefix-free feedback. Our approach combines a recent analysis of a quantizer design for minimum rate LQG control with work on universal lossless source coding for sources on countable alphabets. In the aforementioned quantizer design, it was established that the quantizer outputs are an asymptotically stationary, ergodic process. To enable LQG control with provably near-minimum bitrate, the quantizer outputs must be encoded into binary codewords efficiently. This is possible given knowledge of the probability distributions of the quantizer outputs, or of their limiting distribution. Obtaining such knowledge is challenging; the distributions do not readily admit closed form descriptions. This motivates the application of universal source coding. Our main theoretical contribution in this work is a proof that (after an invertible transformation), the quantizer outputs are random variables that fall within an exponential or power-law envelope class (depending on the plant dimension). Using ideas from universal coding on envelope classes, we develop a practical, zero-delay version of these algorithms that operates with fixed precision arithmetic. We evaluate the performance of this algorithm numerically, and demonstrate competitive results with respect to fundamental tradeoffs between bitrate and LQG control performance.

翻译：我们提出了一种自适应编码方法，以实现线性-二次-高斯（LQG）控制，同时具有近最小比特率的前缀无反馈。我们的方法将针对可数字母表上的源的通用无损源编码工作与最小比特率LQG控制的量化器设计的最新分析相结合。在前述量化器设计中，已经建立了量化器输出是一种渐进稳态，遗传过程的事实。为了实现证明近最小比特率的LQG控制，必须有效地将量化器输出编码为二进制码字。在没有量化器输出的概率分布或极限分布知识的情况下，获得这种知识是具有挑战性的。这激发了通用无损源编码的应用。我们在这项工作中的主要理论贡献是证明（经过一个可逆转换后），量化器输出是落在指数或幂律包络类中的随机变量（取决于植物维度）。使用包络类通用编码思想，我们开发了一种实用的零延迟算法，它使用固定精度算术。我们在数值上评估了该算法的性能，并展示了相对于比特率和LQG控制性能之间的基本权衡的具有竞争力的结果。