A novel prescribed-time H_∞ robust backstepping control algorithm of strict-feedback uncertain nonlinear systems based...

Area of Science:

• Control Theory
• Robotics
• Nonlinear Systems

Background:

• Strict-feedback uncertain nonlinear systems (SFUNSs) present challenges in achieving both rapid convergence and robustness.
• Conventional H∞ robust control methods may face limitations in improving convergence speed without compromising robustness.

Purpose of the Study:

• To develop a novel prescribed-time H∞ robust control scheme for SFUNSs.
• To enhance the convergence speed of robust control systems while preserving their robustness.
• To address lumped uncertainties, including matched and unmatched types, within a prescribed time.

Main Methods:

• A prescribed-time H∞ robust stability theorem was formulated.
• A fuzzy approximation-based controller was designed using a backstepping framework.
• Fuzzy adaptive laws were employed to approximate system uncertainties.
• Lyapunov stability theory was used for theoretical validation.

Main Results:

• The proposed control scheme achieves prescribed-time convergence and robustness for SFUNSs.
• Fuzzy adaptive laws successfully approximate lumped uncertainties in prescribed time.
• The controller demonstrates rapid response performance and strong robustness simultaneously.
• Simulations on a two-link robotic manipulator validated the control scheme's effectiveness.

Conclusions:

• The novel prescribed-time H∞ robust control scheme effectively addresses convergence and robustness challenges in SFUNSs.
• The fuzzy approximation approach enables simultaneous achievement of fast response and strong robustness.
• The method offers a significant improvement over conventional H∞ robust control techniques.