Basis functions, identification and genetic algorithms in norm-optimal iterative learning control

Recently, in (Hatzikos and Owens, 2002b) and (Hatzikos and Owens, 2002a) it was explored whether or not Genetic Algorithm (GAs) based approach can be used in the context of norm-optimal Iterative Learning Control (ILC). It turned out the answer was positive for both linear and nonlinear plant models. However, this approach is still immature in the sense that it can produce very ‘noisy’ intermediate solutions. Furthermore, in practical applications the dimension of the search space can be very large, which can slow down considerably the GA algorithm and increase the computational burden. In order to overcome these problems, in this paper a new basis function approach is proposed. The idea is to restrict the GA search on a proper subspace of the original search space, where the subspace is spanned by a set of orthonormal functions. In this way it is possible to decrease the dimensionality of the search space, and if the basis functions are selected to be ‘smooth’, the search is done only over ‘smooth’ functions. It is in fact shown in this paper that under suitable assumptions, the basis function approach will result in monotonic convergence, which is a very strong property of an ILC algorithm. Furthermore, because the GA needs a simulation model of the plant in question, it is suggested in this paper that the input-output pairs from the ILC trials can be used to identify a model for the plant. Consequently this approach will result in an ILC algorithm with monotonic convergence that requires only an estimate of the order of the plant model. Simulations are used to illustrate the new approach, and they show that the basis function approach combined with identification gives good results in terms of convergence speed and input function smoothness.