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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Lin Chen & Shusheng Bi & Jun Cheng & Yueri Cai & Fanghua Mei, 2022. "Distributed H ∞ and H 2 Time-Varying Formation Tracking Control for Linear Multi-Agent Systems with Directed Topologies," Mathematics, MDPI, vol. 10(18), pages 1-22, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3246-:d:908953
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