Modulated sampled-data consensus for networked Euler-Lagrange systems with differentiable pulse function

Area of Science:

• Control Theory
• Dynamical Systems
• Networked Systems

Background:

• Euler-Lagrange systems are crucial for analyzing dynamical systems.
• Sampled-data feedback in Euler-Lagrange control laws can generate infinite control inputs.
• Existing methods face challenges with discontinuous signals in control law differentiation.

Purpose of the Study:

• To eliminate infinities in control inputs for networked Euler-Lagrange systems.
• To develop applicable control laws using sampled-data feedback.
• To establish a new, less conservative consensus condition.

Main Methods:

• Designing a class of differentiable pulse functions for controllers.
• Utilizing pulse functions as multipliers to render sampled-data signals differentiable.
• Conducting rigorous consensus analysis to derive a new consensus condition.

Main Results:

• Successfully eliminated infinities in control inputs for Euler-Lagrange systems.
• Developed a novel consensus condition compatible with the proposed pulse functions.
• The new consensus condition is demonstrated to be less conservative than existing methods.

Conclusions:

• Differentiable pulse functions effectively resolve infinities in sampled-data Euler-Lagrange control.
• The developed consensus condition enhances control performance and applicability.
• Numerical examples validate the theoretical findings and the effectiveness of the proposed approach.