Deterministic convergence for learning control systems over iteration-dependent tracking intervals

This brief addresses the iterative learning control (ILC) problems for discrete-time systems subject to iteration-dependent tracking time intervals. A modified class of P-type ILC algorithms is proposed by properly defining an available modified output, for which robust convergence analysis is performed with an inductive approach. It is shown that if a persistent full-learning property is ensured, then a necessary and sufficient convergence condition of ILC can be derived to reach the perfect output tracking objective though the tracking time interval is iteration-dependent. That is, the tracking of ILC for iteration-dependent time intervals can be guaranteed in the same deterministic (not stochastic) convergence way as that of traditional ILC over a fixed time interval. Furthermore, the developed tracking results can be extended to admit iteration-dependent uncertainties in initial state and external disturbances. Simulation tests are also included to demonstrate the effectiveness of the modified P-type ILC.