On Self-tuning Property of Variational Adaptive Control Schemes

Abstract

The theory of implicit models. developed in previous papers. is here used in order to define a class of adaptive algorithms based on m-step ahead.or infinite horizon. quadratic optimization. and on Recursive Least Squares identification. even in presence of systems having an ARMAX structure. This can be possible due to the fact that not the true system model but an implicit model is actually sought by the identification procedure. the latter being a model of the system which is correct only in certain closed-loop conditions. In the paper. it is shown that. via the identification of a single extended implicit model (which takes into account the presence of an external dither noise in the control law). and basing on almost no a-priori knowledge about the true system. it is possible to structure the adaptive algorithms in such a way that a single equilibrium point is allowed. coinciding with the optimum control situation