Stability in a novel 3-D chaotic system using optimal generalized back-stepping method

摘要

This paper investigates on control and stabilization of a novel 3_D chaotic system. The chaotic system is stabilized using Generalized Back-stepping Method (GBM); it's similarity to Back-stepping and more applications in systems than it. Back-stepping method is used only to strictly feedback systems but GBM expand this class. The Generalized Back-stepping approach consists of parameters which accept positive value, the system responses differently for each value, It's necessary to select proper parameter to obtain a good response because inappropriate selection lead to the improper responses or even the system unstable for this reason in this text. A series of optimization techniques were applied. To achieve optimal parameters. These optimization techniques are to Genetic Algorithm (GA), Artificial Bee Colony (ABC) And Shuffled Frog Leaping Algorithm (SFLA). In these Algorithms using a minimum squared error cost function. Cost function enforces the system error to decay to zero rapidly. Finally, according to the results of simulations and numerical calculations, we discuss which one of the above algorithms is the best performance and efficiency in the control of the aforementioned system.