Journal
IEEE TRANSACTIONS ON CYBERNETICS
Volume 45, Issue 7, Pages 1315-1326Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCYB.2014.2350511
Keywords
Asymptotic properties; consensus performance; convergence rate; damping rate; distributed consensus protocols; inverse optimality
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Funding
- National Natural Science Foundation of China [61034005, 61433004, 61273148]
- National High Technology Research and Development Program of China [2012AA040104]
- IAPI Fundamental Research Funds [2013ZCX14]
- Development Project of Key Laboratory of Liaoning Province
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In this paper, the inverse optimal approach is employed to design distributed consensus protocols that guarantee consensus and global optimality with respect to some quadratic performance indexes for identical linear systems on a directed graph. The inverse optimal theory is developed by introducing the notion of partial stability. As a result, the necessary and sufficient conditions for inverse optimality are proposed. By means of the developed inverse optimal theory, the necessary and sufficient conditions are established for globally optimal cooperative control problems on directed graphs. Basic optimal cooperative design procedures are given based on asymptotic properties of the resulting optimal distributed consensus protocols, and the multiagent systems can reach desired consensus performance (convergence rate and damping rate) asymptotically. Finally, two examples are given to illustrate the effectiveness of the proposed methods.
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