Implementation of dynamic programming for chaos control in discrete systems

  • Authors:

  • Kaveh Merat;Hassan Salarieh;Aria Alasty

  • Affiliations:

  • Center of Excellence in Design, Robotics and Automation, Department of Mechanical Engineering, Sharif University of Technology, PO Box 11365-9567, Tehran, Iran;Center of Excellence in Design, Robotics and Automation, Department of Mechanical Engineering, Sharif University of Technology, PO Box 11365-9567, Tehran, Iran;Center of Excellence in Design, Robotics and Automation, Department of Mechanical Engineering, Sharif University of Technology, PO Box 11365-9567, Tehran, Iran

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2009

Quantified Score

Hi-index 7.29

Visualization

Abstract

In this paper the control of discrete chaotic systems by designing linear feedback controllers is presented. The linear feedback control problem for nonlinear systems has been formulated under the viewpoint of dynamic programming. For suppressing chaos with minimum control effort, the system is stabilized on its first order unstable fixed point (UFP). The presented method also could be employed to make any desired nth order fixed point of the system, stable. Two different methods for higher order UFPs stabilization are suggested. Afterwards, these methods are applied to two well-known chaotic discrete systems: the Logistic and the Henon Maps. For each of them, the first and second UFPs in their chaotic regions are stabilized and simulation results are provided for the demonstration of performance.