Stability analysis and dynamic regulation of multi-dimensional Taylor network controller for SISO nonlinear systems...

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Systems Theory

Background:

• Existing research on nonlinear systems with time-varying delays often requires complex online optimization.
• Dynamic regulation without online optimization is a significant challenge in advanced control systems.

Purpose of the Study:

• To develop and validate a Multi-Dimensional Taylor Network (MTN) controller for stabilizing single-input single-output (SISO) nonlinear time-varying delay systems.
• To demonstrate that the MTN controller can achieve stabilization through dynamic regulation without necessitating online optimization.

Main Methods:

• Utilized feedback linearization, Lyapunov-Razumikhin theorem, and polynomial approximation theorem.
• Transformed the controller design into a convex optimization problem solvable via appropriate optimization methods.
• Employed the Multi-Dimensional Taylor Network (MTN) controller architecture.

Main Results:

• The MTN controller successfully stabilizes SISO nonlinear time-varying delay systems.
• The controller achieves dynamic regulation of system output without on-line optimization.
• Controller design is simplified through convex optimization, similar to PD-like controllers.
• The MTN controller exhibits independence from the specific system model.

Conclusions:

• The proposed MTN controller offers an effective approach for stabilizing nonlinear systems with time-varying delays.
• The method eliminates the need for computationally intensive online optimization in control system design.
• The controller's model-independence and simplified design process present significant advantages for practical applications.