Equilibrium Stabilization Method to Control Chaotic Behavior of Continuous Systems

Behnam  Babaei; Masoud  Shafiee

doi:10.6180/jase.201903_22(1).0020

Equilibrium Stabilization Method to Control Chaotic Behavior of Continuous Systems

The chaotic behavior of the Lorenz system with initial point (10, 5, 3). (a) x1,x 2 and x3 are unstable vs. time.(b) The trajectory attract to none of fixed points. This system has three fixed points as listed in Table 1.

Behnam Babaei¹ and Masoud Shafiee ¹

¹Department of Electrical Engineering, Amirkabir University of Technology, Iran

Received: January 26, 2018
Accepted: October 2, 2018
Publication Date: March 1, 2019

Download Citation: ||https://doi.org/10.6180/jase.201903_22(1).0020

ABSTRACT

Chaos is a complicated phenomenon in nonlinear dynamical systems. A dynamic controller, based on the stability transformation method (STM), has been used to stabilize both multiple fixed points and unknown unstable periodic orbits (UPOs) in dynamical systems. However, in these methods, there is not any unified algorithm in order to stabilize the fixed points. Here, we present a universal and simple chaos control algorithm called method of selecting an unstable fixed point (SUFP), which is able to stabilize unstable selected fixed points, by generating a stability matrix. Although this algorithm modifies a system by applying an input feedback, the designed feedback does not relocate the positions of fixed points but changes their stabilities. Results show that all tested chaotic trajectories are attracted to selected points, independent of initial values.

Keywords: Stability Matrix, Chaotic System, Fixed Point, Selecting Unstable Fixed Point, SUFP, Eigenvalue, Algorithm, Lorenz Model

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