Adaptive Stabilization of Uncertain Non-Affine Systems with Nonlinear Parameterization

Abstract

This paper investigates the problem of adaptive control for non-affine systems with nonlinear parameterization. Under the controllability-like conditions characterized by the Lie brackets of affine vector fields, we show that there is LgV-type adaptive controllers that globally asymptotically regulate the state of the nonlinearly parameterized system with stable free dynamics while maintaining global stability of the closed-loop system. LgV-type adaptive controllers are designed and their effectiveness is demonstrated by two interesting examples.