High-order PD~α-Type Iterative Learning Control and its Lebesgue-p Norm Convergence

摘要

This paper investigates a high-order PD~α - type iterative learning control strategy for a class of fractional-order linear time-invariant systems with Caputo derivative 0<α<1. On the basis of fractional integration by parts and generalized Young inequality, sufficient convergence condition of the learning control law is established in the sense of Lebesgue-p norm. It is shown that the convergence condition is not only dependent on the fractional-order derivative learning gains, along with the system order, but also dependent on the proportional learning gains and all the matrices associated with the system. Finally, a mumerical example is given to demonstrate the validity of the proposed control law.