Cooperative regulation based on virtual vector triangles asymptotically compressed in multidimensional space for...

Area of Science:

• Control Theory
• Robotics
• Systems Engineering

Background:

• Cooperative control of multi-agent systems is challenging, especially for time-varying nonlinear systems.
• Existing methods often struggle with the complexity and dynamic nature of these systems.

Purpose of the Study:

• To develop a novel distributed adaptive control strategy for time-varying nonlinear multi-agent systems.
• To address the cooperative regulation problem by transforming it into a geometric control problem.

Main Methods:

• Construction of virtual vector triangles in multidimensional space with distributed adaptive virtual points.
• Utilizing spatial coordinate transformation to convert cooperative regulation into virtual triangle compression.
• Designing a distributed compression control protocol based on exponential oscillatory decay.

Main Results:

• The proposed protocol asymptotically shrinks virtual vector triangles towards a common dynamic point.
• Achieved asymptotic convergence consensus for the states of the time-varying nonlinear multi-agent systems.
• Verified stability using a Lyapunov function and Lyapunov stability theory.

Conclusions:

• The virtual vector triangle approach effectively solves the cooperative regulation problem.
• The proposed control protocol demonstrates feasibility and effectiveness through simulations.
• This method offers a novel perspective for controlling complex multi-agent systems.