受控随机动力系统的基本极限：信息论方法
Fundamental Limits of Controlled Stochastic Dynamical Systems: An Information-Theoretic Approach
摘要：
在本文中，我们研究的基本性能限制在随机动力系统的控制，更具体地说，我们推导出通用的$\mathcal{L}_p$界，任何因果（稳定）控制器和任何随机干扰，通过信息理论分析。我们首先考虑工厂（即，被控制的动力系统）是线性时不变的，并且通常可以看出，下界由设备的不稳定极点（或非最小相位零点）以及扰动的条件熵来表征。然后，我们分析的设置，植物被假定为（严格）因果关系，在这种情况下，下界是由条件熵的干扰。我们还讨论了$p = 2$和$p = \infty$的特殊情况，它们分别对应于最小方差控制和最大偏差控制。此外，我们调查的下界的功率谱特征，以及它的关系Kolmogorov-Szegö公式。
英文摘要：
In this paper, we examine the fundamental performance limitations in the control of stochastic dynamical systems; more specifically, we derive generic $\mathcal{L}_p$ bounds that hold for any causal (stabilizing) controllers and any stochastic disturbances, by an information-theoretic analysis. We first consider the scenario where the plant (i.e., the dynamical system to be controlled) is linear time-invariant, and it is seen in general that the lower bounds are characterized by the unstable poles (or nonminimum-phase zeros) of the plant as well as the conditional entropy of the disturbance. We then analyze the setting where the plant is assumed to be (strictly) causal, for which case the lower bounds are determined by the conditional entropy of the disturbance. We also discuss the special cases of $p = 2$ and $p = \infty$, which correspond to minimum-variance control and controlling the maximum deviations, respectively. In addition, we investigate the power-spectral characterization of the lower bounds as well as its relation to the Kolmogorov-Szegö formula.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
