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Cooperative control with distributed gain adaptation and connectivity estimation for directed networks

Authors

  • Zhihua Qu,

    Corresponding author
    1. Department of Electrical Engineering and Computer Science, University of Central Florida, Orlando, FL, USA
    • Correspondence to: Zhihua Qu, Department of Electrical Engineering and Computer Science, University of Central Florida, Orlando, FL 32816, USA.

      E-mail: Qu@ucf.edu

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  • Chaoyong Li,

    1. Department of Electrical Engineering and Computer Science, University of Central Florida, Orlando, FL, USA
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  • Frank Lewis

    1. Automation & Robotics Research Institute, University of Texas, Arlington, TX, USA
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  • This article was published online on 31 August 2012. An error was subsequently identified. This notice is included in the online and print versions to indicate that both have been corrected on 19 September 2012.

SUMMARY

This paper addresses the problem of how to achieve superior performance by adaptively and distributively adjusting control gains of a cooperative control system. It is shown that according to distributed observations of changing network topologies and on the basis of online estimation of network connectivity, cooperative controls with adaptive gains can be synthesized to making the time derivative of the cooperative control Lyapunov function more negative and hence to improve stability and convergence of the overall system. For undirected networks, the proposed adaptive design reduces to improving the Fiedler eigenvalue (algebraic connectivity) as well as other eigenvalues. On the other hand, connectivity of a directed network is characterized by the property of the first left eigenvector(s) associated with its dominant eigenvalue, and in this paper, a distributed high-gain observer design is proposed for each of the networked systems to utilize the same communication network among the systems. It is shown that even in the presence of transmission delays, the distributed estimators converge fast to the first left eigenvector(s) of the network. In addition, the expected consensus value(s) of the overall cooperative system under control is also estimated in a distributive manner. Rigorous analysis is carried out on estimation convergence and observer gain selection. It is shown that the proposed estimation and adaptive control designs are fully distributed, have guaranteed performance for all possible varying topologies as long as their dwelling times are bounded away from zero, and are robust with respect to excessively fast topology changes. Simulation results are included to demonstrate effectiveness of the proposed estimation and control schemes. Copyright © 2012 John Wiley & Sons, Ltd.

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