Switching Prescribed-Time Adaptive Second-Order Sliding Mode Control Subject to Unknown State-Dependent Uncertainties

Area of Science:

• Control Theory
• Nonlinear Systems
• Adaptive Control

Background:

• Nonlinear systems with unknown time-varying parameters present significant control challenges.
• Existing control methods often require prior knowledge of parameter bounds or struggle with both matched and mismatched uncertainties.

Purpose of the Study:

• To propose a novel switching prescribed-time adaptive second-order sliding mode (ASOSM) control framework.
• To address control of nonlinear systems with unknown time-varying parameters and handle both matched and mismatched uncertainties.

Main Methods:

• System transformation using sliding variables to simplify dynamics and reduce uncertainties.
• Design of a switching prescribed-time ASOSM controller using time-scaling and modified adding a power integrator (API) techniques.
• Lyapunov-based stability analysis to guarantee convergence within a prescribed time.

Main Results:

• The proposed ASOSM controller drives sliding variables to a small neighborhood of the origin within a user-assigned prescribed time.
• The system is subsequently stabilized to the equilibrium point in finite time, independent of initial conditions.
• The control scheme effectively handles matched and mismatched uncertainties without needing state-dependent bound information.

Conclusions:

• The developed switching control strategy provides robust and precise control for uncertain nonlinear systems.
• The prescribed-time convergence capability offers enhanced performance and predictability in control system design.
• The framework demonstrates effectiveness through illustrative examples, validating its practical applicability.