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.
Highlights
1 Introduction As a complex system, genetic regulatory networks (GRNs) could describe the complicated regulatory mechanism in living cells, which consist of DNA, RNA, proteins, and some other micro-molecules [1, 2]
The rest of the paper is organized as follows: In Sect. 2, we introduce the models of GRNs at first, and the parameter identification problem is converted into a synchronization problem, some useful lemmas are given
2.2 Description of parameter identification and transformation Noting that in many real situations the parameter matrices A, C, W, and D maybe unknown, we identify those unknown parameters by adaptive synchronization method in this paper
Summary
Genetic regulatory networks (GRNs) could describe the complicated regulatory mechanism in living cells, which consist of DNA, RNA (especially mRNA), proteins, and some other micro-molecules [1, 2]. Parameter identification of solar cell models according to artificial bee swarm optimization algorithm has been investigated in [22]. As for the GRNs, Tang and Wang have considered the problem of parameter identification of unknown delayed GRNs by a switching particle swarm optimization algorithm [24]. There were some results about parameter identification problem for differential equations via adaptive synchronization method. The adaptive laws would be designed to synchronize the auxiliary system to the unknown system. When the synchronization was achieved, the adaptive parameters were supposed to approach the unknown parameters This significant method was proposed by Chen and Lv in [25]. Inspired by the above analysis, this paper studies the parameter identification problem of GRNs with time delay.
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