# Approximate Nonlinear Regulation via Identification-Based Adaptive Internal Models

## TL;DR

This paper introduces an adaptive internal model approach for nonlinear output regulation using system identification, enabling practical regulation without high-gain stabilization and providing bounds based on model prediction accuracy.

## Contribution

It proposes a novel identification-based adaptive internal model for nonlinear regulation that does not rely on high-gain methods and offers practical regulation bounds.

## Key findings

- Practical regulation bounds relate to model prediction accuracy.
- The approach avoids high-gain stabilization.
- Asymptotic regulation occurs when a correct internal model exists.

## Abstract

This paper concerns the problem of adaptive output regulation for multivariable nonlinear systems in normal form. We present a regulator employing an adaptive internal model of the exogenous signals based on the theory of nonlinear Luenberger observers. Adaptation is performed by means of discrete-time system identification schemes, in which every algorithm fulfilling some optimality and stability conditions can be used. Practical and approximate regulation results are given relating the prediction capabilities of the identified model to the asymptotic bound on the regulated variables, which become asymptotic whenever a "right" internal model exists in the identifier's model set. The proposed approach, moreover, does not require "high-gain" stabilization actions.