Moradi Hojjatullah, Majd Vahid Johari
Intelligent Control Systems Laboratory, School of Electrical and Computer Engineering, Tarbiat Modares University, P.O. Box 14115-194, Tehran, Iran.
Intelligent Control Systems Laboratory, School of Electrical and Computer Engineering, Tarbiat Modares University, P.O. Box 14115-194, Tehran, Iran.
Math Biosci. 2016 May;275:10-7. doi: 10.1016/j.mbs.2016.02.006. Epub 2016 Feb 26.
In this paper, the problem of robust stability of nonlinear genetic regulatory networks (GRNs) is investigated. The developed method is an integral sliding mode control based redesign for a class of perturbed dissipative switched GRNs with time delays. The control law is redesigned by modifying the dissipativity-based control law that was designed for the unperturbed GRNs with time delays. The switched GRNs are switched from one mode to another based on time, state, etc. Although, the active subsystem is known in any instance, but the switching law and the transition probabilities are not known. The model for each mode is considered affine with matched and unmatched perturbations. The redesigned control law forces the GRN to always remain on the sliding surface and the dissipativity is maintained from the initial time in the presence of the norm-bounded perturbations. The global stability of the perturbed GRNs is maintained if the unperturbed model is globally dissipative. The designed control law for the perturbed GRNs guarantees robust exponential or asymptotic stability of the closed-loop network depending on the type of stability of the unperturbed model. The results are applied to a nonlinear switched GRN, and its convergence to the origin is verified by simulation.
本文研究了非线性基因调控网络（GRNs）的鲁棒稳定性问题。所提出的方法是一种基于积分滑模控制的重新设计方法，用于一类具有时滞的受扰耗散切换GRNs。通过修改为具有时滞的未受扰GRNs设计的基于耗散性的控制律来重新设计控制律。切换GRNs根据时间、状态等从一种模式切换到另一种模式。虽然在任何时刻活动子系统是已知的，但切换律和转移概率是未知的。每种模式的模型被认为是具有匹配和不匹配扰动的仿射模型。重新设计的控制律迫使GRN始终保持在滑模面上，并且在存在范数有界扰动的情况下从初始时刻起保持耗散性。如果未受扰模型是全局耗散的，则受扰GRNs的全局稳定性得以保持。为受扰GRNs设计的控制律根据未受扰模型的稳定性类型保证闭环网络的鲁棒指数稳定或渐近稳定。将结果应用于一个非线性切换GRN，并通过仿真验证了其收敛到原点。
