Geometric Identification and Control of Nonlinear Dynamic Systems Based on Floating Basis Vector Representation

Abstract

In this paper a simple adaptive controller is outlined that creates only temporal and situation-dependent system model. It may be a plausible alternative of the more sophisticated soft computing approaches that aim the identification of permanent and complete models. The temporal model 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. It may be used for filling in the "lookup tables" or rule bases of the more sophisticated representations experimentally. The method applies simple elimination of the the casual algebraic singularities the occurrence of which cannot be evaded in the practice. The operation of the method is illustrated by the control of a 2 Degrees Of Freedom dynamic system as a typical paradigm via simulation.