论文标题
通过反馈通道编码理论的镜头对线性动力学系统的闭环参数识别
Closed-loop Parameter Identification of Linear Dynamical Systems through the Lens of Feedback Channel Coding Theory
论文作者
论文摘要
本文考虑了具有高斯流程噪声的线性标量系统的闭环识别问题，其中系统输入由确定性状态反馈策略确定。采用了正规化最小二乘估计算法（LSE）算法，试图根据国家无噪声测量结果找到对未知模型参数的最佳估计。我们对从二次控制成本的D-易于标量表标准的意义上讲，可以学习未知参数的速率的基本限制感兴趣。我们首先建立了闭环识别识别问题与涉及带有反馈和一定结构约束的封闭环编码问题之间的新颖联系。基于这一联系，我们表明学习率从根本上是由相应的AWGN通道的能力界定的。尽管反馈政策的最佳设计仍然具有挑战性，但我们得出了实现上限的条件。最后，我们表明所获得的上限意味着超级线性融合对于任何选择的策略都是无法实现的。
This paper considers the problem of closed-loop identification of linear scalar systems with Gaussian process noise, where the system input is determined by a deterministic state feedback policy. The regularized least-square estimate (LSE) algorithm is adopted, seeking to find the best estimate of unknown model parameters based on noiseless measurements of the state. We are interested in the fundamental limitation of the rate at which unknown parameters can be learned, in the sense of the D-optimality scalarization criterion subject to a quadratic control cost. We first establish a novel connection between a closed-loop identification problem of interest and a channel coding problem involving an additive white Gaussian noise (AWGN) channel with feedback and a certain structural constraint. Based on this connection, we show that the learning rate is fundamentally upper bounded by the capacity of the corresponding AWGN channel. Although the optimal design of the feedback policy remains challenging, we derive conditions under which the upper bound is achieved. Finally, we show that the obtained upper bound implies that super-linear convergence is unattainable for any choice of the policy.
