Lyapunov, Adaptive, and Optimal Design Techniques for Cooperative Systems on Directed Communication Graphs

    Authors

    H. W. Zhang; F. L. Lewis;Z. H. Qu

    Comments

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    Abbreviated Journal Title

    IEEE Trans. Ind. Electron.

    Keywords

    Consensus; cooperative control; Laplacian potential; multiagent system; neural adaptive control; optimal control; MULTIAGENT SYSTEMS; MULTIVEHICLE SYSTEMS; CONSENSUS PROBLEMS; NETWORKS; SYNCHRONIZATION; COORDINATION; AGENTS; ALGORITHMS; PASSIVITY; DELAYS; Automation & Control Systems; Engineering, Electrical & Electronic; Instruments & Instrumentation

    Abstract

    This paper presents three design techniques for cooperative control of multiagent systems on directed graphs, namely, Lyapunov design, neural adaptive design, and linear quadratic regulator (LQR)-based optimal design. Using a carefully constructed Lyapunov equation for digraphs, it is shown that many results of cooperative control on undirected graphs or balanced digraphs can be extended to strongly connected digraphs. Neural adaptive control technique is adopted to solve the cooperative tracking problems of networked nonlinear systems with unknown dynamics and disturbances. Results for both first-order and high-order nonlinear systems are given. Two examples, i.e., cooperative tracking control of coupled Lagrangian systems and modified FitzHugh-Nagumo models, justify the feasibility of the proposed neural adaptive control technique. For cooperative tracking control of the general linear systems, which include integrator dynamics as special cases, it is shown that the control gain design can be decoupled from the topology of the graphs, by using the LQR-based optimal control technique. Moreover, the synchronization region is unbounded, which is a desired property of the controller. The proposed optimal control method is applied to cooperative tracking control of two-mass-spring systems, which are well-known models for vibration in many mechanical systems.

    Journal Title

    Ieee Transactions on Industrial Electronics

    Volume

    59

    Issue/Number

    7

    Publication Date

    1-1-2012

    Document Type

    Article

    Language

    English

    First Page

    3026

    Last Page

    3041

    WOS Identifier

    WOS:000300510500028

    ISSN

    0278-0046

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