Evolutionary synthesis of rules for stabilization of selected discrete chaotic systems

Abstract

This research deals with a utilization of tool for symbolic regression, which is analytic programming, for the purpose of the synthesis of a new control laws. These synthesized chaotic controllers secure the stabilization of stable state of four selected discrete chaotic system. The systems of interest were the one-dimensional noninvertible map (Cubic map) and three examples of two-dimensional dissipative maps (Lozi, Burgers and Delayed Logistic map). The paper consists of the descriptions of analytic programming as well as chaotic systems, used heuristic and cost function. For experimentation, Self-Organizing Migrating Algorithm (SOMA) and Differential evolution (DE) were used.