IEEE Trans Neural Netw Learn Syst. 2018 Feb;29(2):299-309. doi: 10.1109/TNNLS.2016.2618899. Epub 2016 Nov 14.
This paper addresses the problem of state estimation for delayed genetic regulatory networks (DGRNs) with reaction-diffusion terms using Dirichlet boundary conditions. The nonlinear regulation function of DGRNs is assumed to exhibit the Hill form. The aim of this paper is to design a state observer to estimate the concentrations of mRNAs and proteins via available measurement techniques. By introducing novel integral terms into the Lyapunov-Krasovskii functional and by employing the Wirtinger-type integral inequality, the convex approach, Green's identity, the reciprocally convex approach, and Wirtinger's inequality, an asymptotic stability criterion of the error system was established in terms of linear matrix inequalities (LMIs). The stability criterion depends upon the bounds of delays and their derivatives. It should be noted that if the set of LMIs is feasible, then the desired observation of DGRNs is possible, and the state estimation can be determined. Finally, two numerical examples are presented to illustrate the availability and applicability of the proposed scheme design.
本文针对具有狄利克雷边界条件的时滞基因调控网络（DGRN），利用反应扩散项解决了状态估计问题。假设 DGRN 的非线性调节函数呈现出 Hill 形式。本文旨在设计一个状态观测器，通过可用的测量技术来估计 mRNA 和蛋白质的浓度。通过在李雅普诺夫-克拉索夫斯基泛函中引入新的积分项，并利用 Wirtinger 型积分不等式、凸方法、格林恒等式、互凸方法和 Wirtinger 不等式，基于线性矩阵不等式（LMIs）建立了误差系统的渐近稳定性判据。稳定性判据取决于时滞及其导数的界。需要注意的是，如果 LMI 集是可行的，那么 DGRN 的期望观测是可能的，并且可以确定状态估计。最后，给出了两个数值示例来说明所提出方案设计的有效性和适用性。
