Synchronization of a Non-Equilibrium Four-Dimensional Chaotic System Using a Disturbance-Observer-Based Adaptive...

Area of Science:

• Nonlinear Dynamics
• Chaos Theory
• Control Systems Engineering

Background:

• Investigates a non-equilibrium four-dimensional chaotic system characterized by hidden attractors and a plane of equilibria.
• Highlights unique dynamical features including invariance, symmetry, dissipativity, and offset boosting.

Purpose of the Study:

• To analyze the dynamical behavior of the novel chaotic system.
• To develop and validate a robust adaptive control strategy for synchronization.
• To address challenges like noise, disturbances, and control input saturation.

Main Methods:

• Analysis of system dynamics, including invariance, symmetry, and attractor properties.
• Design of a disturbance-observer-based adaptive terminal sliding mode control (ATSMC) method.
• Integration of an extended Kalman filter (EKF) for noise reduction.
• Optimization of controller parameters using a genetic algorithm to mitigate chattering.
• Application of Lyapunov stability theory for finite-time convergence guarantees.

Main Results:

• The proposed ATSMC method ensures finite-time synchronization of the chaotic system.
• The integrated EKF effectively handles system noise and disturbances.
• Genetic algorithm optimization successfully reduced chattering phenomena.
• Numerical simulations confirm the controller's robustness against input saturation and external disturbances.

Conclusions:

• The developed control scheme provides effective and robust synchronization for the studied chaotic system.
• The combination of ATSMC, EKF, and genetic algorithm optimization offers a powerful approach for controlling complex chaotic dynamics.
• The findings contribute to advancing control strategies for chaotic systems in practical applications.