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This paper studies the immersion and invariance (I&I) adaptive trackingproblem for a class of nonlinear systems with nonlinear parameterization in theISS framework. Under some mild assumptions, a novel I&I adaptive controlalgorithm is proposed,leading to an interconnection of an ISS estimation errorsubsystem and an ISS tracking error subsystem. Using an ISS small-gaincondition, the desired uniform global asymptotic stability of the resultinginterconnected "error" system can be achieved and a sum-type strict Lyapunovfunction can be explicitly constructed. Taking advantage of this ISS-baseddesign framework,it is shown that the corresponding robustness with respect tothe input perturbation can be rendered to be ISS. To remove the need to solvethe immersion manifold shaping PDE, a new filter-based approach is proposed,which preserves the ISS-based design framework. Finally, we demonstrate thevalidness of the proposed framework on a tracking problem for series elasticactuators.

Robust I&I Adaptive Tracking Control of Systems with Nonlinear Parameterization: An ISS Perspective