A Gradient Dynamics-Based Singularity Avoidance Method for Backstepping Control of Underactuated TORA Systems.

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics

Background:

• Backstepping control design for systems like the TORA system often encounters singularity problems.
• These singularities can lead to control law discontinuities and performance degradation.

Purpose of the Study:

• To propose a novel gradient dynamics-based control method to address the singularity issue in backstepping control for the TORA system.
• To ensure system stability and improve tracking performance.

Main Methods:

• Developed an energy-like positive function incorporating an auxiliary variable related to the virtual control law.
• Created a gradient dynamics to generate a new virtual control command that drives the auxiliary variable to zero.
• Integrated gradient dynamics into the recursive backstepping framework.
• Employed Lyapunov-based stability analysis to prove uniform ultimate boundedness of closed-loop signals and convergence of tracking errors.

Main Results:

• The proposed method effectively mitigates the division-by-zero issue inherent in traditional backstepping.
• Demonstrated avoidance of singularity problems in simulations.
• Achieved superior transient performance compared to existing methods.
• Rigorous analysis confirmed system stability and error convergence.

Conclusions:

• The gradient dynamics-based control offers a robust solution to singularity problems in TORA system backstepping.
• The method enhances control system performance and stability.
• This approach provides a valuable alternative for nonlinear control design challenges.