Observer-based event-triggered control for semilinear time-fractional diffusion systems with distributed feedback

  • Fudong GeEmail author
  • YangQuan Chen
Original paper


This paper is concerned with the observer-based distributed event-triggered feedback control for semilinear time-fractional diffusion systems under the Robin boundary conditions. To this end, an extended Luenberger-type observer is presented to solve the limitations caused by the impossible availability of full-state information that is needed for feedback control in practical applications due to the difficulties of measuring. With this, we propose the distributed output feedback event-triggered controllers via backstepping technique under which the considered systems admit Mittag–Leffler stability. It is shown that the given event-triggered control strategy could significantly reduce the amount of transmitted control inputs while guaranteeing the desired system performance with the Zeno phenomenon being excluded. A numerical illustration is finally presented to illustrate our theoretical results.


Event-triggered control Semilinear time-fractional diffusion systems Mittag–Leffler stabilization Robin boundary conditions Backstepping 



This work was supported by the National Natural Science Foundation of China (NSFC) under Grants 61907039 and 41801365, the Hubei NSFC under Grant 2019CFB255 and the Fundamental Research Funds for the Central Universities, China University of Geosciences, Wuhan, under grant CUGGC05.

Compliance with ethical standards

Conflict of interest

It is worth noting that the brief version of this paper without any detailed proofs has been submitted to NODYCON 2019, the First International Dynamics Conference in Rome at February 17–20, 2019. In other words, this paper can be regarded as the substantially expanded version of the previous conference paper. In addition to this, the authors declare that there is no conflict of interest regarding the publication of this paper.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of Computer ScienceChina University of GeosciencesWuhanPeople’s Republic of China
  2. 2.Department of Mechanical Engineering (MESA-Lab)University of CaliforniaMercedUSA

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