Convergence Properties of Iterative Learning Control Processes in the Sense of the Lebesgue-P Norm

Abstract

This paper addresses the convergence issue of first-order and second-order PD-type iterative learning control schemes for a type of partially known linear time-invariant systems. By taking advantage of the generalized Young inequality of convolution integral, the convergence is analyzed in the sense of the Lebesgue-p norm and the convergence speed is also discussed in terms of Qp factors. Specifically, we find that: (1) the sufficient condition on convergence is dominated not only by the derivative learning gains, along with the system input and output matrices, but also by the proportional learning gains and the system state matrix; (2) the strictly monotone convergence is guaranteed for the first-order rule while, in the case of the second-order scheme, the monotonicity is maintained after some finite number of iterations; and (3) the iterative learning process performed by the second-order learning scheme can be Qp-faster, Qp-equivalent, or Qp-slower than the iterative learning process manipulated by the first-order rule if the learning gains are appropriately chosen. To manifest the validity and effectiveness of the results, several numerical simulations are conducted