On Controllability of Neuronal Networks With Constraints on the Average of Control Gains

Yang Tang, Zidong Wang, Huijun Gao, Hong Qiao, Jurgen Kurths

Research output: Contribution to journalArticlepeer-review

48 Citations (Scopus)


Control gains play an important role in the control
of a natural or a technical system since they reflect how much
resource is required to optimize a certain control objective. This
paper is concerned with the controllability of neuronal networks
with constraints on the average value of the control gains injected
in driver nodes, which are in accordance with engineering and
biological backgrounds. In order to deal with the constraints on
control gains, the controllability problem is transformed into a
constrained optimization problem (COP). The introduction of the
constraints on the control gains unavoidably leads to substantial
difficulty in finding feasible as well as refining solutions. As such,
a modified dynamic hybrid framework (MDyHF) is developed
to solve this COP, based on an adaptive differential evolution
and the concept of Pareto dominance. By comparing with
statistical methods and several recently reported constrained
optimization evolutionary algorithms (COEAs), we show that our
proposed MDyHF is competitive and promising in studying the
controllability of neuronal networks. Based on the MDyHF, we
proceed to show the controlling regions under different levels of
constraints. It is revealed that we should allocate the control gains
economically when strong constraints are considered. In addition,
it is found that as the constraints become more restrictive, the
driver nodes are more likely to be selected from the nodes with
a large degree. The results and methods presented in this paper
will provide useful insights into developing new techniques to
control a realistic complex network efficiently.
Original languageEnglish
Pages (from-to)2670-2681
Number of pages12
JournalIEEE Transactions on Cybernetics
Issue number12
Early online date11 Apr 2014
Publication statusPublished - Dec 2014


  • complex networks
  • controllability
  • evolutionary algorithms
  • multiagent systems
  • neural networks
  • synchronization/consensus


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