Multiple Lyapunov Functions for Adaptive Neural Tracking Control of Switched Nonlinear Nonlower-Triangular Systems

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Artificial Intelligence

Background:

• Adaptive control is crucial for uncertain nonlinear systems.
• Switched and nonlower-triangular systems pose significant control challenges.
• Existing methods often require restrictive assumptions on system dynamics.

Purpose of the Study:

• To develop adaptive neural tracking control for uncertain switched nonlinear nonlower-triangular systems.
• To remove the input-to-state stability assumption for unmodeled dynamics.
• To overcome design complexities associated with nonlower-triangular structures.

Main Methods:

• Utilizing radial basis function neural networks for universal approximation.
• Employing Gaussian function properties to manage nonlower-triangular structures.
• Applying multiple Lyapunov functions within a backstepping-like recursive design.

Main Results:

• Successfully removed the input-to-state stability requirement for unmodeled dynamics.
• Developed a controller that handles nonlower-triangular systems without restrictive bounding functions.
• Ensured all closed-loop system signals remain bounded.
• Achieved convergence of tracking error to a small neighborhood of the origin.

Conclusions:

• The proposed adaptive neural tracking control is effective for uncertain switched nonlinear nonlower-triangular systems.
• The method offers a more general approach by relaxing previous assumptions.
• Simulation examples validate the practicability and feasibility of the control design.