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access icon free Distributed H ∞ and H 2 consensus control in directed networks

  • Author(s): Jingyao Wang 1 ; Zhisheng Duan 1 ; Zhongkui Li 1 ; Guanghui Wen 2
    • View affiliations
    • Affiliations: 1: State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, People's Republic of China;
      2: Department of Mathematics, Southeast University, Nanjing 210096, People's Republic of China
  • Source: Volume 8, Issue 3, 13 February 2014, p. 193 – 201
    DOI:  10.1049/iet-cta.2013.0258 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Received 26/03/2013, Accepted 24/09/2013, Revised 16/07/2013, Published 10/12/2013

In this study, the H ∞ consensus problem of a group of linear multi-agent systems with directed communication graph is addressed. To achieve H ∞ consensus, a new class of distributed consensus protocols based only on the relative states of the neighbouring agents is proposed. Compared with the existing protocols, the one presented in this study focuses on solving the H ∞ consensus problem in strongly connected directed networks. By using tools from algebraic graph theory and Lyapunov stability analysis, it is theoretically shown that distributed H ∞ consensus in the closed-loop multi-agent systems with strongly connected topology can be achieved if the distributed consensus protocol is appropriately designed. A two-step algorithm is then presented to construct such a protocol. The H 2 consensus problem for networked systems is further investigated. Finally, the effectiveness of the theoretical analysis is verified via numerical simulations.

Inspec keywords: stability; H∞ control; algebra; directed graphs; Lyapunov methods; multi-agent systems

Other keywords: topology; linear multiagent systems; closed loop multiagent systems; algebraic graph theory; distributed consensus protocols; Lyapunov stability analysis; directed networks; two step algorithm; directed communication graph; H infinity consensus problem; networked systems; H infinity consensus control; numerical simulations

Subjects: Expert systems and other AI software and techniques; Algebra; Stability in control theory; Combinatorial mathematics; Optimal control

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