论文标题
受控随机动力学系统的基本限制：一种信息理论方法
Fundamental Limits of Controlled Stochastic Dynamical Systems: An Information-Theoretic Approach
论文作者
论文摘要
在本文中，我们研究了控制随机动力学系统的基本绩效限制。更具体地说，我们通过信息理论分析得出了适用于任何因果（稳定）控制器和任何随机干扰的通用$ \ Mathcal {l} _p $界限。我们首先考虑植物（即要控制的动态系统）是线性时间流动的情况，并且通常可以看出，下限的特征是植物的不稳定极（或非最小相相的零）以及干扰的条件入口。然后，我们分析假定植物为（严格）因果关系的设置，在这种情况下，下限是由干扰的条件熵确定的。我们还讨论了$ p = 2 $和$ p = \ infty $的特殊情况，分别对应于最小值控制和控制最大偏差。此外，我们研究了下限的功率 - 光谱表征及其与Kolmogorov-Szegö公式的关系。
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.
