Convergence analysis of PIβDα-type fractional-order iterative learning control in the sense of Lp norm

The convergence of PI^βD^α-type fractional-order iterative learning control(FOILC) is discussed for a class of fractional-order linear time-invariant system in the sense of L^p norm. First, by taking advantage of the generalized Young inequality of convolution integral, the sufficient conditions for the monotone convergence of first and second-order PI^βD^α-type control laws are analyzed in the sense of L^p norm, and generalizes to the convergence condition of N-th-order PI^βD^α-type control law. Then the convergence speeds of first and second-order PI^βD^α-type ILC are compared. The analysis indicates that the convergence is determined not only by the learning gains of control law, but also by the attributes of the system itself. The simulation results validate the correctness of the theory and the feasibility of the proposed control law.