Robust convergence analysis of iterative learning control for impulsive Riemann-Liouville fractional-order systems

摘要

In this paper, we explore P-type learning laws for impulsive Riemann-Liouville fractional-order controlled systems ( 0 α 1 ) $(0lpha1)$ with initial state offset bounded to track the varying reference accurately by using a few iterations in a finite time interval. By using the Gronwall inequality and fundamental inequalities, we obtain open-loop and closed-loop P-type robust convergence results in the sense of ( P C 1 − α , λ ) $(PC_{1-lpha}, lambda)$ -norm ∥ ⋅ ∥ P C 1 − α , λ $|cdot|_{PC_{1-lpha},lambda}$ . Finally, numerical examples are given to illustrate our theoretical results.