# Hybrid Direct-Indirect Adaptive Control of Nonlinear System with Unmatched Uncertainty

## TL;DR

This paper introduces a hybrid adaptive control method combining direct and indirect strategies to effectively manage nonlinear systems with both matched and unmatched uncertainties, improving robustness and tracking performance.

## Contribution

The paper proposes a novel hybrid MRAC architecture that estimates unmatched uncertainties online and integrates them into the control design for nonlinear systems.

## Key findings

- Successfully estimates unmatched uncertainties online
- Achieves reference model tracking in nonlinear systems
- Handles a broad class of systems with uncertainties

## Abstract

In this paper, we present a hybrid direct-indirect model reference adaptive controller (MRAC), to address a class of problems with matched and unmatched uncertainties. In the proposed architecture, the unmatched uncertainty is estimated online through a companion observer model. Upon convergence of the observer, the unmatched uncertainty estimate is remodeled into a state dependent linear form to augment the nominal system dynamics. Meanwhile, a direct adaptive controller designed for a switching system cancels the effect of matched uncertainty in the system and achieves reference model tracking. We demonstrate that the proposed hybrid controller can handle a broad class of nonlinear systems with both matched and unmatched uncertainties