Continuous control of chaos based on the stability criterion

Area of Science:

• Nonlinear Dynamics and Control
• Chaos Theory
• System Stabilization

Background:

• Chaotic systems are prevalent in science and engineering but difficult to control.
• Existing chaos control methods often require linearization or precise orbit knowledge.
• Stabilizing chaotic systems onto desired periodic orbits remains a significant challenge.

Purpose of the Study:

• To propose a novel chaos control method based on a stability criterion.
• To demonstrate the stabilization of chaotic systems onto desired periodic orbits using nonlinear feedback.
• To highlight the flexibility and convenience of the proposed control method.

Main Methods:

• A time-continuous perturbation nonlinear feedback is applied.
• The method utilizes a stability criterion for control.
• It does not require linearization around the target orbit.
• Approximate location of the desired periodic orbit is sufficient and automatically detected.

Main Results:

• The proposed method successfully stabilizes chaotic systems onto desired periodic orbits.
• Numerical examples demonstrate effectiveness in controlling spacecraft attitude motion, the Rössler system, and coupled Duffing oscillators.
• The control can be initiated at any moment under specific conditions.

Conclusions:

• The developed chaos control method offers a flexible and convenient approach.
• It effectively stabilizes chaotic systems without needing linearization or exact orbit information.
• The method shows broad applicability across various complex dynamical systems.