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 Q p 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 Q p -faster, Q p -equivalent, or Q p -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.

The paper develops a derivative-type (D-type) networked iterative learning control (NILC) scheme for repetitive discrete-time systems with packet dropouts stochastically occurred in input and output communication channels. The scheme generates the sequential recursive-mode control inputs by mending the dropped instant-wise output with the synchronous desired output, while it drives the plant by refreshing the dropped instant-wise control input with the used consensus-instant control input at the previous iteration. By adopting statistic technique, the convergences of the developed NILC scheme for linear and nonlinear systems are derived, respectively. The derivations present that under certain conditions the mathematical expectations of the stochastic tracking errors in the sense of 1-norm converge to zero. Numerical simulations exhibit the effectiveness and validity.

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This paper develops two proportional-type (P-type) networked iterative learning control (NILC) schemes for a class of discrete-time nonlinear systems whose stochastic output packet dropouts are modeled as 0-1 Bernoulli stochastic sequences. In constructing the NILC schemes, two kinds of compensation algorithm of the dropped outputs are given. One is to replace the instant-wise dropped output data with the synchronous desired output data; the other is to substitute the dropped data with the consensus-instant output data used at the previous iteration. By adopting the lifting technique, it is derived that under certain conditions the expectations of the tracking errors incurred by the proposed NILC schemes converge to zero along the iteration axis. Numerical experiments are carried out for validity and effectiveness.