Information-Theoretic Performance Limitations of Feedback Control: Underlying Entropic Laws and Generic $\mathcal{L}_{p}$ Bounds
This work provides foundational limits for feedback control, impacting all of ML/AI, though it is incremental in extending information-theoretic principles to generic systems.
The paper tackles the problem of establishing fundamental performance limits for generic feedback control systems, deriving $\mathcal{L}_p$ bounds on control error that are characterized by the conditional entropy of disturbances, based on inherent entropic laws.
In this paper, we utilize information theory to study the fundamental performance limitations of generic feedback systems, where both the controller and the plant may be any causal functions/mappings while the disturbance can be with any distributions. More specifically, we obtain fundamental $\mathcal{L}_p$ bounds on the control error, which are shown to be completely characterized by the conditional entropy of the disturbance, based upon the entropic laws that are inherent in any feedback systems. We also discuss the generality and implications (in, e.g., fundamental limits of learning-based control) of the obtained bounds.