Immersion and invariance adaptive control of a class of nonlinear systems with unknown control direction

Abstract

The goal of this article is to extend the adaptive control problem of parametric strict feedback form nonlinear systems, using immersion and invariance to the case of unknown, possibly, time-varying control direction. The idea is to immerse a target system in ℝ n−1, which is stabilised through the design of virtual controllers, into an extended system in ℝ n+p . The designed controller takes advantage of the well-known Nussbaum functions to deal with the unknown sign of input multiplier and is designed through the manifold dynamics belonging to ℝ p+1. The effectiveness of the proposed method is shown through a simulation example and is also compared to the classical adaptive backstepping approach with an unknown control direction.