From geometric invariants and symbolic matrixes towards new perspectives on forecasting of PWM converter dynamics

In this paper the fractal method of nonlinear dynamics forecasting regarding PWM converters is developed by transition towards symbolic modelling. Previously, within the fractal method bounds the technique of combining of several forms of dynamics description (in the form of periodic process domains in a bifurcation diagram and in the form of time series) into one special space was presented [Chaos, Solitons and Fractals 2005;23(1), 24(3), 25(5)]. It was answered positively on the question about the possibility of estimation of transient convergence direction in real-time mode. Now, presentation of a dynamic process is proposed as the consecution of geometric invariants. Correspondingly, the symbolical model of a periodic process represents the combination of limited number of the invariants and a transient can be analyzed through the deviations from this model. As a result, it becomes possible to forecast the direction of transient convergence under parametric uncertainties, that is important in relation to the considered class of piece-wise dynamic systems. The proposed method is illustrated by computer simulations.