  This paper studies the immersion and invariance (I&I) adaptive tracking
problem for a class of nonlinear systems with nonlinear parameterization in the
ISS framework. Under some mild assumptions, a novel I&I adaptive control
algorithm is proposed,leading to an interconnection of an ISS estimation error
subsystem and an ISS tracking error subsystem. Using an ISS small-gain
condition, the desired uniform global asymptotic stability of the resulting
interconnected "error" system can be achieved and a sum-type strict Lyapunov
function can be explicitly constructed. Taking advantage of this ISS-based
design framework,it is shown that the corresponding robustness with respect to
the input perturbation can be rendered to be ISS. To remove the need to solve
the immersion manifold shaping PDE, a new filter-based approach is proposed,
which preserves the ISS-based design framework. Finally, we demonstrate the
validness of the proposed framework on a tracking problem for series elastic
actuators.
