Distributed H ∞ and H 2 Time-Varying Formation Tracking Control for Linear Multi-Agent Systems with Directed Topologies

Lin Chen, Shusheng Bi, Jun Cheng, Yueri Cai () and Fanghua Mei
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Lin Chen: Robotics Institute, School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China
Shusheng Bi: Robotics Institute, School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China
Jun Cheng: Robotics Institute, School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China
Yueri Cai: Robotics Institute, School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China
Fanghua Mei: Robotics Institute, School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China

Mathematics, 2022, vol. 10, issue 18, 1-22

Abstract: In this paper, the H ∞ and H 2 time-varying formation tracking problems for multi-agent systems with directed topologies in the presence of external disturbances are investigated. The followers need to achieve the desired time-varying formation during movement and simultaneously track the state trajectory generated by the leader. First, a distributed consensus protocol based on the local state information of neighbors of the agents for solving H ∞ and H 2 time-varying formation tracking problems are proposed without utilizing global information about the entire agents. The conditions to achieve H ∞ and H 2 time-varying formation tracking in the presence of external disturbances are suggested respectively. Then, to determine the parameters of the designed protocol which satisfy suitable conditions, algorithms for H ∞ and H 2 time-varying formation tracking in the form of pseudo-code are presented, respectively. Furthermore, the proofs of the proposed theorems are derived by utilizing algebraic graph theory and Lyapunov analysis theory tools to demonstrate the closed-loop stability of the system in the presence of external disturbances. Finally, the usefulness and effectiveness of the approaches proposed are demonstrated by numerical simulation examples.

Keywords: time-varying formation tracking; multi-agent system; external disturbances; robust H ? and H 2 performance; Lyapunov stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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