High-Order Sliding Mode Control Design Subject to Unknown Nonvanishing Uncertainties

Area of Science:

• Control Theory
• Nonlinear Systems
• Robotics

Background:

• Nonvanishing uncertainties pose significant challenges in controlling nonlinear systems.
• Existing sliding mode control (SMC) methods often require knowledge of disturbance upper bounds, limiting their applicability.

Purpose of the Study:

• To propose a novel high-order SMC method for nonlinear systems with nonvanishing uncertainties.
• To develop a control strategy that does not require prior knowledge of uncertainty upper bounds.

Main Methods:

• Introduction of a low-order virtual integral dynamics to reconstruct system dynamics.
• Design of an SMC law with correction terms using Lyapunov theory to manage disturbances with unknown upper bounds.

Main Results:

• The proposed SMC method effectively handles nonvanishing uncertainties without requiring their upper bounds.
• Finite-time convergence of the closed-loop system is mathematically guaranteed.
• The method's efficacy is demonstrated through its application to a Buck converter system.

Conclusions:

• The developed high-order SMC offers a robust solution for controlling nonlinear systems with persistent, unknown uncertainties.
• This approach advances control methodologies by removing the constraint of known disturbance bounds.
• The successful application to a Buck converter validates the practical utility of the proposed control strategy.