Fundamental Entropic Laws and $\mathcal{L}_p$ Limitations of Feedback Systems: Implications for Machine-Learning-in-the-Loop Control

In this paper, we study the fundamental performance limitations for generic feedback systems in which both the controller and the plant may be arbitrarily causal while the disturbance can be with any distributions. In particular, we obtain fundamental $\mathcal{L}_p$ bounds based on the entropic laws that are inherent in any feedback systems. We also examine the implications of the generic bounds for machine-learning-in-the-loop control; in other words, fundamental limits in general exist to what machine learning elements in feedback loops can achieve.