Regulation without calibration

TL;DR

This paper explores regulation methods in control systems, contrasting trajectory and event regulation, highlighting the internal model principle's calibration challenges, and proposing event regulation as a more practical alternative.

Contribution

It introduces the concept of event regulation as a way to relax calibration requirements in control systems while maintaining reliability of discrete events.

Findings

Trajectory regulation requires exact internal models, leading to calibration challenges.

Event regulation can achieve regulation objectives without precise internal models.

Event regulation offers a practical alternative to trajectory regulation in control systems.

Abstract

This article revisits the importance of the internal model principle in the literature of regulation and synchronization. Trajectory regulation, the task of regulating continuous-time signals generated by differential equations, is contrasted with event regulation, the task of only regulating discrete events associated with the trajectories. In trajectory regulation, the internal model principle requires an exact internal generator of the continuous-time trajectories, which translates into unrealistic calibration requirements. Event regulation is envisioned as a way to relieve calibration of the continuous behavior while ensuring reliability of the discrete events.