Stabilization of logical control networks: an event-triggered control approach

Abstract

This paper investigates the global stabilization problem of k-valued logical control networks (KVLCNs) via event-triggered control (ETC), where the control inputs only work at several certain individual states. Compared with traditional state feedback control, the designed ETC approach not only shortens the transient period of logical networks but also decreases the number of controller executions. The content of this paper is divided into two parts. In the first part, a necessary and sufficient criterion is derived for the event-triggered stabilization of KVLCNs, and a construction procedure is developed to design all time-optimal event-triggered stabilizers. In the second part, the switching-cost-optimal event-triggered stabilizer is designed to minimize the number of controller executions. A labeled digraph is obtained based on the dynamic of the overall system. Utilizing this digraph, we formulate a universal and unified procedure called the minimal spanning in-tree algorithm to minimize the triggering event set. Furthermore, we illustrate the effectiveness of obtained results through several numerical examples.

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Acknowledgements

This work was partially supported by National Natural Science Foundation of China (Grant Nos. 11671361, 61833005, 61573096), Natural Science Foundation of Zhejiang Province (Grant No. LD19A010001), Natural Science Foundation of Jiangsu Province (Grant No. BK20170019), and Jiangsu Provincial Key Laboratory of Networked Collective Intelligence (Grant No. BM2017002).

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Correspondence to Yang Liu or Jinde Cao.

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Zhu, S., Liu, Y., Lou, Y. et al. Stabilization of logical control networks: an event-triggered control approach. Sci. China Inf. Sci. 63, 112203 (2020). https://doi.org/10.1007/s11432-019-9898-3

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Keywords

  • logical control network
  • event-triggered control
  • stabilization
  • semi-tensor product
  • minimal spanning in-tree