  This paper generalizes recent results by the authors on noninvasive
model-reference adaptive control designs for control-based continuation of
periodic orbits in periodically excited linear systems with matched
uncertainties to a larger class of periodically excited nonlinear systems with
matched uncertainties and known structure. A candidate adaptive feedback design
is also proposed in the case of scalar problems with unmodeled nonlinearities.
In the former case, rigorous analysis shows guaranteed performance bounds for
the associated prediction and estimation errors. Together with an assumption of
persistent excitation, there follows asymptotic convergence to periodic
responses determined uniquely by an a priori unknown periodic reference input
and independent of initial conditions, as required by the control-based
continuation paradigm. In particular, when the reference input equals the
sought periodic response, the steady-state control input vanishes. Identical
conclusions follow for the case of scalar dynamics with unmodeled
nonlinearities, albeit with slow rates of convergence. Numerical simulations
validate the theoretical predictions for individual parameter values.
Integration with the software package COCO demonstrate successful continuation
along families of stable and unstable periodic orbits with a minimum of
parameter tuning. The results expand the envelope of known noninvasive feedback
strategies for use in experimental model validation and engineering design.
