Synchronization of chaotic systems with known and unknown parameters using a modified active sliding mode control

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Chaos Theory

Background:

• Synchronization of chaotic systems is crucial for applications like secure communications.
• Parametric uncertainty and measurement noise pose significant challenges in achieving robust synchronization.
• Existing sliding mode control methods can be complex and sensitive to uncertainties.

Purpose of the Study:

• To develop a new active sliding mode surface for synchronizing two chaotic systems with parametric uncertainty.
• To simplify the controller design process compared to classical approaches.
• To ensure robust stability of the error dynamics under noisy conditions.

Main Methods:

• Definition of a novel integral acting surface for active sliding mode control.
• Assignment of appropriate eigenvalues to control error dynamics.
• Development of a sufficient condition for robust stability.
• Simulation studies to validate the proposed control strategy.

Main Results:

• The proposed integral acting surface simplifies controller parameter calculation.
• The method effectively synchronizes chaotic systems despite parametric uncertainty and measurement noise.
• Robust stability of the error dynamics is achieved.

Conclusions:

• The novel active sliding mode surface offers a simpler and more robust approach to chaotic system synchronization.
• The proposed control strategy is effective and reliable in the presence of uncertainties and noise.
• This work contributes to the advancement of robust chaos control techniques.