Estimation-based Norm-optimal Iterative Learning Control, Report no. LiTH-ISY-R-3066

The iterative learning control (ilc) method improves performance of systems that repeat the same task several times. In this paper the standard norm-optimal ilc control law for linear systems is extended to an estimation-based ilc algorithm where the controlled variables are not directly available as measurements. The proposed ilc algorithm is proven to be stable and gives monotonic convergence of the error. The estimationbased part of the algorithm uses Bayesian estimation techniques such as the Kalman lter. The objective function in the optimisation problem is modi ed to incorporate not only the mean value of the estimated variable, but also information about the uncertainty of the estimate. It is further shown that for linear time-invariant systems the ilc design is independent of the estimation method. Finally, the concept is extended to non-linear state space models using linearisation techniques, where it is assumed that the full state vector is estimated and used in the ilc algorithm. It is also discussed how the Kullback-Leibler divergence can be used if linearisation cannot be performed. Finally, the proposed solution for non-linear systems is applied and veri ed in a simulation study with a simpli ed model of an industrial manipulator system.