Stabilization of Port Hamiltonian Chaotic Systems with Hidden Attractors by Adaptive Terminal Sliding Mode Control

Area of Science:

• Nonlinear Dynamics and Control Systems
• Chaos Theory and Complex Systems
• Port Hamiltonian Systems

Background:

• Chaotic systems with hidden attractors pose significant stabilization challenges.
• Port Hamiltonian systems offer a structured framework for analyzing complex dynamics.
• Existing control methods may not effectively address the unique properties of hidden attractors.

Purpose of the Study:

• To design an adaptive terminal sliding mode controller (ATSMC) for stabilizing port Hamiltonian chaotic systems with hidden attractors.
• To develop a methodology for designing chaotic oscillators with hidden attractors within a topological framework.
• To ensure system state stability and suppress chaotic behavior in the targeted systems.

Main Methods:

• Design of a 2-D chaotic oscillator using a topological framework.
• Conversion of the chaotic oscillator into a port Hamiltonian system for analysis.
• Formulation of an adaptive terminal sliding mode controller using a Lyapunov approach.
• Development of online control and adaptive laws for stability and chaos suppression.

Main Results:

• Successful design of a chaotic oscillator exhibiting hidden attractors.
• Conversion of the oscillator into a port Hamiltonian system for detailed analysis.
• Development and validation of an adaptive terminal sliding mode controller.
• Demonstration of the controller's effectiveness in stabilizing chaotic states and suppressing chaos.

Conclusions:

• The proposed adaptive terminal sliding mode controller effectively stabilizes port Hamiltonian chaotic systems with hidden attractors.
• The Lyapunov-based approach ensures online system stability and chaos suppression.
• The study verifies theoretical findings through empirical tests, confirming the controller's efficacy.