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This paper investigates the learning ability of iterative learning control (ILC) system with a randomly varying trial length (RVTL). The randomness of trial length is modelled as a discrete stochastic sequence. Firstly, we study the output controllability of the control system over a finite time interval. It is shown that the control system is completely controllable if and only if the input–output coupling matrix (IOCM) is full-row rank. Secondly, we propose an intermittent learning scheme with state feedback. It is strictly proved that under appropriate constraints on the learning gain and the IOCM, the ILC system with RVTL has full learning ability if and only if the probability that the trial length is equal to the desired one is greater than zero. There must exist state feedback such that the ILC process is monotonically convergent. Meanwhile, we illustrate that the proposed convergence conditions can ensure the almost sure convergence property of system output. Finally, an example is given to illustrate the merits of the ILC system with state feedback.

Learning ability of iterative learning control system with a randomly varying trial length