Abstract

In this paper, the parameter identification of gene regulatory network with time-varying delay is studied. Firstly, we introduce the differential equation model of gene regulatory network with unknown parameters and time delay. Secondly, for the unknown parameters in the time-varying model, a corresponding system with adaptive parameters and adaptive controller is introduced, and the parameter identification problem of the original model is transformed into the synchronization problem of the two systems. Thirdly, we design an effective adaptive controller and an adaptive law for parameters and construct a Lyapunov functional. Then we give a strict theoretical proof that the adaptive parameters can converge to unknown parameters by Barbalat’s lemma. Finally, a numerical example is given to verify the validity of the theoretical results.

中文翻译：

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时滞遗传调节网络参数自适应自适应辨识

摘要

本文研究了具有时变时延的基因调控网络的参数辨识。首先，介绍了未知参数和时滞的基因调控网络的微分方程模型。其次，针对时变模型中的未知参数，引入了具有自适应参数和自适应控制器的对应系统，并将原始模型的参数辨识问题转化为两个系统的同步问题。第三，设计了有效的自适应控制器和参数自适应律，并构造了一个Lyapunov函数。然后我们给出了严格的理论证明，即自适应参数可以通过Barbalat引理收敛到未知参数。最后，通过数值例子验证了理论结果的正确性。