System identification in the repetition domain

Procedures for system identification using realization theory in conjunction with learning control ideas are developed. The Markov parameters of the system are identified by combining data from repeated experiments. Three approaches are discussed for identification of as many Markov parameters as sample points in the experiment. Making use of all the parameters, realization theory is then employed to determine the system order and to obtain a minimal order representation. The first two approaches are non-recursive, which in the case of noise-free data yields a one step solution. The third approach uses a recursive formulation rendered from adaptive control but modified for successive experiments. A simple example shows the numerical convergence of the identified parameters as a function of the number of experiments. The procedure presented herein is an extension of the existing Eigensystem Realization Algorithm (ERA), which has been successfully applied for system identification of large structures.