A new subspace based approach to iterative learning control

This paper¹ presents an iterative learning control (ILC) procedure based on an inverse model of the plant under control. Our first contribution is that we formulate the inversion procedure as a Kalman smoothing problem: based on a compact state space model of a possibly non-minimum phase system, identified by the MOESP class of subspace identification methods, we determine the inverse model. The inverse model gives an output sequence which is the solution of a generalized least squares problem. The method does no longer suffer from missing knowledge of the state (initial and end), optimally deals with both process and measurement noise, and is able to deal with non-square and non-stationary systems. Our second contribution is that the method is coupled with subspace identification in an optimal way, i.e. once the state space model of the system is identified, a low order compact inverse model follows. In case of divergence of the ILC process, re-identification is applied and we provide a qualitative analysis in which we show that the re-identification has a stabilizing influence on the ILC process, which is our third contribution. A control simulation example on a complex mechanical structure is provided to demonstrate the potential of the algorithm.