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

Area of Science:

• Control Theory
• Systems Engineering
• Robotics

Background:

• Multiagent systems (MASs) present challenges in coordinated control, especially when leader information is unavailable to followers.
• Projective vortex formation tracking (PVFT) is a complex task requiring sophisticated control strategies for linear systems operating on directed graphs.

Purpose of the Study:

• To develop a distributed adaptive observer and a novel PVFT protocol for linear MASs.
• To address the challenge of unknown leader input and its upper bound in follower systems.
• To enable precise tracking and formation control in MASs under directed graph topologies.

Main Methods:

• Design of a distributed adaptive observer utilizing projection matrices to estimate leader virtual signals.
• Proposal of a distributed PVFT protocol incorporating distributed and local observers with coordinate coupling matrices.
• Implementation of adaptive update mechanisms and nonlinear functions to handle unknown leader inputs.
• Development of an algorithm to prove the PVFT protocol through estimation, aggregation, and rotation processes.

Main Results:

• The proposed distributed adaptive observer successfully captures desired virtual signals of the leader.
• The novel distributed PVFT protocol enables linear MASs to achieve formation tracking.
• The algorithm ensures reliable PVFT through systematic estimation, aggregation, and rotation.
• Analysis of parameter effects on aggregation and rotation demonstrates protocol robustness.

Conclusions:

• The study successfully demonstrates a reliable method for achieving PVFT in linear MASs with limited information.
• The developed observer and protocol offer a significant advancement in distributed control for multiagent systems.
• The findings have implications for coordinating robotic systems and other MAS applications requiring precise formation control.