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Exponential stabilization of chaotic systems with delay by periodically intermittent control
Chuandong Li1, Xiaofeng Liao, Tingwen Huang
1School of Computer, Hangzhou Dianzi University, Hangzhou 310018, China. licd@cqu.edu.cn
Chaos (Woodbury, N.Y.)
|April 7, 2007
Summary
This study stabilizes chaotic systems with time delays using periodically intermittent control. A new stability criterion and controller design are verified through simulations on chaotic oscillators.
Area of Science:
- Control Theory
- Nonlinear Dynamics
- Chaos Theory
Background:
- Chaotic systems exhibit sensitive dependence on initial conditions, making their control challenging.
- Time delays in chaotic systems can further complicate stabilization efforts.
- Intermittent control offers a potential strategy for managing complex systems with reduced control effort.
Purpose of the Study:
- To investigate the exponential stabilization of chaotic systems with time delays.
- To develop a unified criterion for assessing the stability of such systems under intermittent control.
- To design a suboptimal intermittent controller for fixed control periods.
Main Methods:
- Lyapunov function and differential inequality techniques were employed to establish stability criteria.
- A suboptimal intermittent controller was designed based on a general cost function.
- Numerical simulations were conducted on two distinct chaotic oscillators.
Main Results:
- A unified exponential stability criterion for delayed chaotic systems under intermittent control was successfully derived.
- Simplified versions of the stability criterion were also presented.
- The designed suboptimal controller demonstrated effectiveness in simulations.
Conclusions:
- Periodically intermittent control is an effective method for achieving exponential stabilization in chaotic systems with delays.
- The developed theoretical framework provides a robust approach for analyzing and controlling complex dynamical systems.
- The findings offer valuable insights for the practical implementation of control strategies in chaotic systems.
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