  Barrier Lyapunov functions are suitable for learning control designs, due to
their feature of finite duration tracking. This paper presents fractional
barrier Lyapunov functions, provided and compared with the conventional ones in
the error-constraint learning control designs. Two error models are adopted and
the desired compensation control approach is applied for a non-parametric
design, allowing two kinds of uncertainties involved in the error dynamics.
Theoretical results about existence of the solution and convergence of the
learning control schemes are presented. It is shown that fully-saturated
learning algorithms play important role in assuring boundedness of the
estimates, by which the error constraint objective can be achieved. Moreover,
the robust technique is developed through modifying the discontinuous action
involved in the learning control scheme that yields the expected tracking
performance in the presence of residual.
