Stochastic iterative learning control for discrete linear time-invariant system with batch-varying reference trajectories

Abstract

In this paper, we present adaptive iterative learning control (ILC) schemes for discrete linear time-invariant (LTI) stochastic system with batch-varying reference trajectories (BVRT). If reference trajectories change every batch, ILC shows a different convergence property from that of the identical reference trajectory. First, we derive the convergence property and propose deterministic adaptive ILC combined with iterative learning identification for LTI system with BVRT. If the state noise and measurement noise exist, convergence rate and tracking performance are degraded because the controller considers the difference arising from the noise as tracking error. To deal with such a problem, we propose two approaches. The first is based on a batch-domain Kalman filter, which uses the difference between the current output trajectory and the next reference trajectory as a state vector, while the second is based on a time-domain Kalman filter. In the second approach, the system is identified at the end of each batch in an iterative fashion using the observer/Kalman filter identification (OKID). Then, the stochastic problem is handled using Kalman filter with a steady-state Kalman gain obtained from the identification. Therefore, the second approach can track the reference trajectories of discrete LTI stochastic system using only the input–output information. Simulation examples are provided to show the effectiveness of the proposed schemes.