Journal
INTERNATIONAL JOURNAL OF CONTROL
Volume 85, Issue 8, Pages 1039-1050Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00207179.2012.674644
Keywords
multi-agent system; distributed control; robustness; H-infinity control; parameter uncertainty
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Funding
- Natural Science Foundation of China [61104153, 60974078]
- Major State Basic Research Development Program [2012CB720000]
- China Postdoctoral Science Foundation [20100480211, 201104059]
- Research Fund for the Doctoral Program of Higher Education of China [20091101110025]
- Singapore-MIT Alliance for Research and Technology (SMART) Centre [FM-06]
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This article considers the distributed robust control problems of uncertain linear multi-agent systems with undirected communication topologies. It is assumed that the agents have identical nominal dynamics while subject to different norm-bounded parameter uncertainties, leading to weakly heterogeneous multi-agent systems. Distributed controllers are designed for both continuous-and discrete-time multi-agent systems, based on the relative states of neighbouring agents and a subset of absolute states of the agents. It is shown for both the continuous-and discrete-time cases that the distributed robust control problems under such controllers in the sense of quadratic stability are equivalent to the H-infinity control problems of a set of decoupled linear systems having the same dimensions as a single agent. A two-step algorithm is presented to construct the distributed controller for the continuous-time case, which does not involve any conservatism and meanwhile decouples the feedback gain design from the communication topology. Furthermore, a sufficient existence condition in terms of linear matrix inequalities is derived for the distributed discrete-time controller. Finally, the distributed robust H-infinity control problems of uncertain linear multi-agent systems subject to external disturbances are discussed.
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