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Volume 9 Issue 5
May  2022

IEEE/CAA Journal of Automatica Sinica

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Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2022  >  9(5): 864-877
W. C. Huang, H. L. Liu, and  J. Huang,  “Distributed robust containment control of linear heterogeneous multi-agent systems: An output regulation approach,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 5, pp. 864–877, May 2022. doi: 10.1109/JAS.2022.105560
Citation: W. C. Huang, H. L. Liu, and  J. Huang,  “Distributed robust containment control of linear heterogeneous multi-agent systems: An output regulation approach,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 5, pp. 864–877, May 2022. doi: 10.1109/JAS.2022.105560
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Distributed Robust Containment Control of Linear Heterogeneous Multi-Agent Systems: An Output Regulation Approach

doi: 10.1109/JAS.2022.105560
Funds:  This work was supported by the National Science Foundation of China (51977040)
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    Abstract

  • In this paper, we consider the robust output containment problem of linear heterogeneous multi-agent systems under fixed directed networks. A distributed dynamic observer based on the leaders’ measurable output was designed to estimate a convex combination of the leaders’ states. First, for the case of followers with identical state dimensions, distributed dynamic state and output feedback control laws were designed based on the state-coupled item and the internal model compensator to drive the uncertain followers into the leaders’ convex hull within the output regulation framework. Subsequently, we extended theoretical results to the case where followers have nonidentical state dimensions. By establishing virtual errors between the dynamic observer and followers, a new distributed dynamic output feedback control law was constructed using only the states of the compensator to solve the robust output containment problem. Finally, two numerical simulations verified the effectiveness of the designed schemes.

     

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    • 1 This paper has two types of dynamic output feedback law, the footnote is to distinguish so as not to confuse.
    2 This footnote is for the same purpose as Footnote 1.
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    Highlights

    • For the robust output containment control problem with the uncertain followers of identical nominal dynamics, based on the internal model principle and the compensator technique, the distributed dynamic state and output feedback control laws were introduced to drive the uncertain followers to enter the convex hull spanned by the leaders under the output regulation framework. Among them, the nonsingular transformation and a Lyapunov inequality method was used to analysis the closed-loop system stabilization
    • By introducing the distributed observer systems, we extended the theoretical results to a more general case where the followers have nonidentical state dimensions. In this section, the robust containment problem was converted into a new tracking problem between the distributed observer systems and the follower systems by constructing a virtual error. A distributed dynamic output feedback control law was further devised to drive the virtual error to converge to the origin asymptotically, such that multi-agent systems achieved output containment control
    • At present, most of the containment control protocols must know the relative values of the state with respect to its neighbors, so they can only deal with the situation with followers having the same state dimensions. In our research, the distributed control law has avoided the dependence on the relative states of followers by utilizing the virtual error, and is capable of solving the robust output containment problem for linear heterogeneous multi-agent systems with nonidentical state dimensions
    • We modify the conventional state observer to produce an estimate of the convex combination of the leaders’ states by applying a directed network, which lends itself to the design of the distributed protocols. Moreover, the distributed observer can also be viewed as an extension of the compensators associated with the leaders’ states in some relevant literature, because these compensators can be regarded as a special case of our observer when the output matrix of the leader systems is of full column rank

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