Iterative learning control with time-partitioned update for collaborative output tracking

This article studies iterative learning control (ILC) where multiple heterogeneous linear subsystems (with potentially different individual dynamics) update their input simultaneously based on the error in a collaboratively controlled desired output. A challenge is that convergence of iterative learning for each individual subsystem (when the other subsystems are not learning) may not guarantee convergence under collaborative-(co-) learning. This work proposes an update-partitioning approach for co-learning and demonstrates convergence whenever the individual, iterative learning for each subsystem is convergent. The main contribution of this work is to show that any unity partition (where the sum of the partition is one) of the update law ensures convergence of the co-learning. Since the time partitioning of the update can be chosen independent of the individual learning (convergence) rate of the subsystems, the proposed approach enables the separate design of each individual subsystem's input-update law followed by conjoining of the individual update laws for co-learning using the partitioning approach. Additionally, an intermittent time partitioning is developed when the desired trajectory is not known to all (but only some) of the co-learning subsystems.