Robust Output Regulation of Uncertain Linear Time-Varying Systems

TL;DR

This paper introduces a new systematic framework for robust output regulation of uncertain linear time-varying systems, emphasizing an intrinsic system immersion approach that simplifies controller design and handles uncertainties effectively.

Contribution

It proposes a novel intrinsic system immersion method, extends the regulator equation analysis, and offers a systematic way to design robust controllers without explicitly solving the regulator equation.

Findings

Robust control is achievable without explicitly solving the regulator equation.

The approach extends to coordinate-free frameworks and non-resonance conditions.

The method reduces the dimension of the internal model needed for regulation.

Abstract

Robust output regulation for linear time-varying systems has remained an open problem for decades. To address this, we propose intrinsic system immersion by reformulating the regulator equation in a more insightful form, indicating that finding an internal model is equivalent to reproducing the output trajectory of a forced system by constructing an unforced system. This perspective reveals the influence of parametric uncertainties, demonstrating that an infinite-dimensional controller is generally unavoidable for robustness against plant uncertainty. Consequently, a general robust design is proposed without explicitly solving the regulator equation. It ensures robustness against uncertainties in the exosystem interaction, and achieves approximate output regulation when an infinite-dimensional controller is necessary for regulation. Additionally, we study the regulator equation in a coordinate-free framework, extend the time-varying non-resonance condition, and provide a method to minimize the dimension of an internal model. Overall, these results provide a general systematic framework for constructing robust internal model-based controllers, and simplify the control implementation process.