ISS method for coordination control of nonlinear dynamical agents under directed topology

Area of Science:

• Control Systems Engineering
• Robotics
• Networked Systems

Background:

• Multiagent systems with second-order nonlinear dynamics present coordination challenges, especially under directed interaction topologies.
• Existing methods struggle with locally Lipschitz continuous dynamics and directed graph structures.

Purpose of the Study:

• To develop a robust coordination framework for multiagent systems with second-order locally Lipschitz continuous nonlinear dynamics.
• To address coordination under directed interaction topologies, tackling inherent technical difficulties.

Main Methods:

• A nonlinear input-to-state stability (ISS)-based framework is proposed.
• Leverages graph theory, matrix theory, and the ISS cyclic-small-gain theorem.
• Applies the framework to flocking with a virtual leader and containment control problems.

Main Results:

• The proposed ISS framework effectively coordinates agents with locally Lipschitz continuous dynamics under directed topologies.
• For flocking, coordination is achieved if at least one agent in each strongly connected component with zero in-degree accesses leader information.
• For containment control, agents are guaranteed to converge to the convex hull of leaders if each agent has a directed path from a leader.

Conclusions:

• The developed ISS framework provides a unified and effective approach for complex multiagent coordination problems.
• The results demonstrate the framework's capability to handle directed interaction topologies and nonlinear dynamics, ensuring flocking and containment control.