Comparative analysis of two adaptive controls based on geometric principles of identification and the extension of the modified renormalization transformation

In this paper two simple adaptive controllers are outlined that create only temporal and situation-dependent system models. They may be plausible alternatives of the more sophisticated soft computing approaches that aim at the identification of permanent and complete models. In both cases the temporal models can be built up and maintained step-by-step on the basis of slow elimination of fading information by the use of simple updating rules consisting of finite algebraic steps of lucid geometric interpretation, but in quite different manners. Both methods apply simple elimination of the casual algebraic singularities the occurrence of which cannot be evaded in the practice. The operation of the methods is illustrated by the control of a 2-degrees-of-freedom dynamic system as a typical paradigm via simulation