Iterative Learning Control of Stochastic Linear Systems with Reference Trajectory Switching

A reference trajectory is specified for systems that repetitively execute the same finite duration task in iterative learning control. In many current designs, the reference signal remains the same, but in others, it is desirable to allow the reference trajectory to change during the system’s overall operation. This paper develops a control law design method for linear dynamics where the measured signals are noise corrupted, random disturbances are present, and the reference trajectory is allowed to change during operation. The new design is based on the recently developed stochastic stability theory for repetitive processes, a class of 2D systems, and uses vector Lyapunov functions and their divergence properties. It also shows how to eliminate the transient error that results from a switch of the reference trajectory. A numerical case study demonstrates the applicability of the new design.