Sampled-data-based consensus and containment control of multiple harmonic oscillators: A motion-planning approach.

Area of Science:

• Control Systems Engineering
• Networked Systems
• Robotics

Background:

• Distributed systems require coordination for tasks like consensus and containment.
• Harmonic oscillators are fundamental models in physics and engineering.
• Directed communication topologies present challenges in achieving coordinated behavior.

Purpose of the Study:

• To develop novel distributed consensus protocols for harmonic oscillators under directed communication.
• To design distributed containment protocols for harmonic oscillators with multiple leaders.
• To demonstrate the decoupling of sampling periods, communication topologies, and control gains in sampled-data systems.

Main Methods:

• Utilizing motion planning and Pontryagin's principle for consensus protocol design.
• Applying stability theory and stochastic matrix properties to prove consensus.
• Developing containment protocols based on leader-follower dynamics.
• Employing sampled-data control strategies.

Main Results:

• A novel distributed consensus protocol requiring only relative measurements at sampling instants was developed.
• The consensus problem was proven solvable within the motion planning framework.
• Distributed containment protocols were designed for followers to converge to the leaders' convex hull.
• The proposed protocols decouple sampling periods, communication topologies, and control gains.

Conclusions:

• The developed protocols effectively solve distributed consensus and containment problems for harmonic oscillators.
• The sampled-data-based approach offers significant advantages by decoupling design parameters.
• The findings relax restrictions in controller design for networked systems.