  Learning to perform perfect tracking tasks based on measurement data is
desirable in the controller design of systems operating repetitively. This
motivates the present paper to seek an optimization-based design approach for
iterative learning control (ILC) of repetitive systems with unknown nonlinear
time-varying dynamics. It is shown that perfect output tracking can be realized
with updating inputs, where no explicit model knowledge but only measured
input/output data are leveraged. In particular, adaptive updating strategies
are proposed to obtain parameter estimations of nonlinearities. A
double-dynamics analysis approach is applied to establish ILC convergence,
together with boundedness of input, output, and estimated parameters, which
benefits from employing properties of nonnegative matrices. Moreover, robust
convergence is explored for optimization-based adaptive ILC in the presence of
nonrepetitive uncertainties. Simulation tests are also implemented to verify
the validity of our optimization-based adaptive ILC.
