Universal Adaptive Control of Nonlinear Systems

TL;DR

This paper introduces a universal adaptive control framework for nonlinear systems with unmatched uncertainties, dynamically adjusting adaptation rates to ensure stability and compatibility with existing feedback policies.

Contribution

It extends the certainty equivalence principle to nonlinear systems with unmatched uncertainties and incorporates online adaptation rate adjustment for improved stability.

Findings

Successfully applied to various nonlinear systems with uncertainties

Eliminates parameter estimation transients affecting stability

Compatible with existing feedback policies

Abstract

This work develops a new direct adaptive control framework that extends the certainty equivalence principle to general nonlinear systems with unmatched model uncertainties. The approach adjusts the rate of adaptation online to eliminate the effects of parameter estimation transients on closed-loop stability. The method can be immediately combined with a previously designed or learned feedback policy if a corresponding model-parameterized Lyapunov function or contraction metric is known. Simulation results of various nonlinear systems with unmatched uncertainties demonstrates the approach.