Finite and infinite horizon LQ adaptive controllers based on implicit model identification

A shortened list of the basic results about implicit modelling theory and its application for adaptive control is provided. This theory deals with the possibility of representing systems driven by proper feedback laws by means of models which are structurally different from the true model, and simpler to be identified. The relevance of this subject derives from the possibility of devising adaptive control algorithms based on the identification of relatively simple models, which admit the optimum control situation as an equilibrium point.