Iterative Learning Control of Stochastic Linear Systems under Switching of the Reference Trajectory and Parameters

摘要

The paper develops a new iterative learning control (ILC) law for a system in which the reference trajectory and system parameters change between passes in a known manner, the control plant is subjected to random disturbances, and measurements are carried out with noise. The design is based on the recently developed stochastic stability theory of repetitive processes, that are a class of 2D systems. This theory uses vector Lyapunov functions and their divergence to obtain stabilization conditions. In this paper the proposed method of vector Lyapunov functions is used in combination with Kalman filtering. For reducing the transient error caused by the reference trajectory change, the ILC law switches, depending on this change. A supporting example is given, demonstrating that this law yields a significant reduction of the transient error, that generated by the reference trajectory change.