Inversion of linear square systems by learning

The problem of inverting a linear square system by means of a learning approach is addressed. Algorithms are given which compute, by successive trails on the real plant, the initial conditions and the input required to track a desired output exactly. Depending upon the given tracking problem, both time-domain and frequency-domain analysis are developed. A model-based algorithm is proposed and its robustness investigated. For minimum-phase systems a high-gain scheme is presented. Some examples illustrate the applicability of the algorithms and the possible trade-off between rate of convergence and robustness