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Chaos / Volume 22 / Issue 1 / REGULAR ARTICLES

Chaos 22, 013120 (2012); http://dx.doi.org/10.1063/1.3683487 (8 pages)

Stabilization of chaos systems described by nonlinear fractional-order polytopic differential inclusion

Saeed Balochian1 and Ali Khaki Sedigh2

1Gonabad Branch, Islamic Azad University, Gonabad, Iran
2Department of Electrical and Computer Engineering, K. N. Toosi University of Technology, Tehran, Iran

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(Received 14 August 2011; accepted 21 January 2012; published online 16 February 2012)

In this paper, sliding mode control is utilized for stabilization of a particular class of nonlinear polytopic differential inclusion systems with fractional-order-0 < q < 1. This class of fractional order differential inclusion systems is used to model physical chaotic fractional order Chen and Lu systems. By defining a sliding surface with fractional integral formula, exploiting the concept of the state space norm, and obtaining sufficient conditions for stability of the sliding surface, a special feedback law is presented which enables the system states to reach the sliding surface and consequently creates a sliding mode control. Finally, simulation results are used to illustrate the effectiveness of the proposed method.

© 2012 American Institute of Physics

Lead Paragraph

The main point of this paper is stabilization of nonlinear fractional order polytopic differential inclusion systems. These systems are very important for modeling of chaos fractional order systems such as Chen, Lu, and Rossler systems. The main contributions of the paper can be summarized as follows:
  • The control of chaos systems described by nonlinear fractional-order polytopic differential inclusion systems and elimination of the input disturbance.
  • Design of a new state feedback law for the nonlinear fractional order polytopic differential inclusion systems for stabilization.
  • Lyapunov based convergence proof for the control law in finite time.
  • Illustrative simulation results to show the effectiveness of the proposed methodology.

Article Outline

  1. INTRODUCTION
  2. PRELIMINARIES
    1. Fractional order derivative and integral
  3. PROBLEM FORMULATION
  4. MAIN RESULTS
  5. SIMULATION RESULTS
  6. CONCLUSION

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KEYWORDS, PACS, and IPC

Keywords

chaos, nonlinear differential equations, stability, state-space methods, variable structure systems

PACS

  • 05.45.Gg

    Control of chaos, applications of chaos

  • 02.60.Lj

    Ordinary and partial differential equations; boundary value problems

International Patent Classification (IPC)

  • G05B17/00

    Systems involving the use of models or simulators of said systems

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3683487

PUBLICATION DATA

ISSN

1054-1500 (print)  
1089-7682 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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