西安交通大学教师主页管理系统阮小娥 CONVERGENCE PROPERTIES OF ITERATIVE LEARNING CONTROL PROCESSES IN THE SENSE OF THE LEBESGUE-P NORM Home

CONVERGENCE PROPERTIES OF ITERATIVE LEARNING CONTROL PROCESSES IN THE SENSE OF THE LEBESGUE-P NORM

Release Time:2025-04-30

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Title of Paper:: CONVERGENCE PROPERTIES OF ITERATIVE LEARNING CONTROL PROCESSES IN THE SENSE OF THE LEBESGUE-P NORM

Summary:: This paper addresses the convergence issue of first-order and secondorder
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.