Retraction Notice: Multiple Transformation Matrix-Based Adaptive Projective Vortex Formation Tracking for Multiagent...

Area of Science:

• Control Systems Engineering
• Robotics
• Networked Systems

Background:

• Multiagent systems (MASs) often face challenges in coordinated control, especially when leader information is unavailable to followers.
• Projective vortex formation tracking (PVFT) is a complex control objective requiring sophisticated algorithms for decentralized systems.

Purpose of the Study:

• To develop a distributed adaptive observer and a novel PVFT protocol for linear MASs on directed graphs.
• To address the challenge of unknown leader input and its upper bound in follower systems.

Main Methods:

• Design of a distributed adaptive observer using projection matrices to estimate leader signals.
• Proposal of a distributed PVFT protocol incorporating distributed and local observers with coordinate coupling.
• Implementation of adaptive update mechanisms and nonlinear functions to handle unknown leader inputs.

Main Results:

• The proposed protocol, under a specific algorithm, successfully achieves PVFT through estimation, aggregation, and rotation.
• Systematic analysis of parameter effects on aggregation and rotation dynamics.
• Validation of the results through several simulation examples.

Conclusions:

• The developed distributed adaptive observer and PVFT protocol are effective for linear MASs with unknown leader information.
• The findings provide a reliable method for achieving coordinated control in decentralized systems.
• The study demonstrates the feasibility and reliability of the proposed approach in complex multiagent scenarios.