Predefined-time sliding mode control of chaotic systems based on disturbance observer.

Area of Science:

• Control Theory
• Nonlinear Dynamics
• Chaos Theory

Background:

• Chaotic systems are highly sensitive to initial conditions and external factors.
• Controlling chaotic systems with uncertainties and disturbances is a significant challenge.
• Existing control methods may not guarantee convergence within a predefined time.

Purpose of the Study:

• To develop a novel control strategy for n-dimensional chaotic systems.
• To achieve predefined-time stability and tracking control despite disturbances and uncertainties.
• To provide a method for precisely setting the convergence time for chaotic system control.

Main Methods:

• Design of a disturbance observer to estimate and compensate for system uncertainties.
• Development of a sliding mode controller for robust system stabilization.
• Formulation of a sliding manifold to ensure predefined-time error convergence.
• Utilization of two predefined-time parameters to determine the total convergence time.

Main Results:

• The proposed method successfully stabilizes the error system on the sliding manifold within a predefined time.
• The dynamical system reaches the sliding surface within the specified predefined time.
• Demonstrated feasibility and effectiveness of the combined disturbance observer and sliding mode control approach.
• The convergence time is adjustable by presetting specific parameters.

Conclusions:

• The presented disturbance observer and sliding mode control method effectively achieves predefined-time control for n-dimensional chaotic systems.
• The approach offers enhanced robustness against disturbances and uncertainties.
• The ability to predefine convergence time provides precise control over system behavior.