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Optimal Linear and Nonlinear Control Design for Chaotic Systems

[+] Author Affiliations
Marat Rafikov

Universidade Regional do Noroeste do Estado Rio Grande do Sul, Ijui, RS, Brazil

José Manoel Balthazar

Universidade Estadual Paulista, Rio Claro, SP, Brazil

Paper No. DETC2005-84998, pp. 867-873; 7 pages
  • ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 6: 5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C
  • Long Beach, California, USA, September 24–28, 2005
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4743-8 | eISBN: 0-7918-3766-1
  • Copyright © 2005 by ASME


In this work, the linear and nonlinear feedback control techniques for chaotic systems were been considered. The optimal nonlinear control design problem has been resolved by using Dynamic Programming that reduced this problem to a solution of the Hamilton-Jacobi-Bellman equation. In present work the linear feedback control problem has been reformulated under optimal control theory viewpoint. The formulated Theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations for the Rössler system and the Duffing oscillator are provided to show the effectiveness of this method.

Copyright © 2005 by ASME
Topics: Design



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