Dynamic scaling-based adaptive control without scaling factor: With application to Euler–Lagrange systems

A modular dynamic scaling-based immersion and invariance (I&I) adaptive control framework for a class of nonlinear system with parametric uncertainties is presented in this paper. The framework is based on an invariant manifold approach which allows for predefined target dynamics to be assigned to the closed-loop systems. The integrability obstacle typically inherent to I&I methodology is overcome by the matrix reconstruction and dynamic scaling technique. The prominent feature is that this methodology can be implemented without scaling factor, and hence the introduction of the scaling factor is just to prove the additive disturbance brought by the matrix reconstruction can be eliminated by constant feedback gains. Moreover, the bounded robustness against three different types of disturbance is verified. As an application, Euler-Lagrange systems with unknown inertia parameters are applied to illustrate the effectiveness of the proposed method.