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Linear optimal control of continuous time chaotic systems.

Kaveh Merat1, Jafar Abbaszadeh Chekan1, Hassan Salarieh1

  • 1Department of Mechanical Engineering, Sharif University of Technology, P.O. Box 11155-9567, Tehran, Iran.

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This study suppresses chaos in continuous time systems using dynamic programming. A novel method converts systems to discrete types, enabling chaos control in chaotic models like Rossler and AFM.

Keywords:
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Area of Science:

  • Nonlinear Dynamics and Control Systems Engineering
  • Computational Mathematics and Applied Science

Background:

  • Chaos control is crucial for stabilizing unpredictable dynamic systems.
  • Traditional methods often face challenges with continuous-time chaotic systems.

Purpose of the Study:

  • To develop and apply a dynamic programming technique for chaos control in continuous-time systems.
  • To convert continuous chaotic systems into discrete forms for effective control.
  • To demonstrate the efficacy of the proposed method on benchmark chaotic systems.

Main Methods:

  • Utilizing Poincare sections and linear regression to transform continuous systems into discrete ones.
  • Solving the Riccati equation to devise a sub-optimal control algorithm for discrete chaotic systems.
  • Implementing the algorithm on quantized continuous-time systems to suppress chaos.

Main Results:

  • Successfully converted continuous-time chaotic systems to discrete equivalents.
  • Developed and applied a sub-optimal dynamic programming algorithm for chaos suppression.
  • Demonstrated effective chaos suppression in the Rossler and AFM systems.

Conclusions:

  • The dynamic programming approach effectively controls chaos in continuous-time systems.
  • The conversion to discrete systems via Poincare sections and linear regression is a viable strategy.
  • The proposed method offers a robust technique for stabilizing chaotic behavior in engineering applications.