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

Fractional Barrier Lyapunov Functions with Application to Learning Control