Robust control of uncertain nonlinear switched genetic regulatory networks with time delays: A redesign approach.

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.

[1]  Yong He,et al.  Robust stabilization and H(∞) controllers design for stochastic genetic regulatory networks with time-varying delays and structured uncertainties. , 2012, Mathematical biosciences.

[2]  V. J. Majd,et al.  Stability analysis of disturbed switched systems , 2011, The 2nd International Conference on Control, Instrumentation and Automation.

[3]  I. M. de la Fuente.  Quantitative Analysis of Cellular Metabolic Dissipative, Self-Organized Structures , 2010, International journal of molecular sciences.

[4]  Yeung Sam Hung,et al.  Stability analysis of uncertain genetic sum regulatory networks , 2008, Autom..

[5]  Jean-Luc Gouzé,et al.  Exact control of genetic networks in a qualitative framework: The bistable switch example , 2011, Autom..

[6]  Indranil Saha,et al.  journal homepage: www.elsevier.com/locate/neucom , 2022 .

[7]  L. Serrano,et al.  Engineering stability in gene networks by autoregulation , 2000, Nature.

[8]  Huijun Gao,et al.  New passivity results for uncertain discrete-time stochastic neural networks with mixed time delays , 2010, Neurocomputing.

[9]  Yonghui Sun,et al.  Stochastic stability of Markovian switching genetic regulatory networks , 2009 .

[10]  Zidong Wang,et al.  Sampled‐data H∞ filtering for stochastic genetic regulatory networks , 2011 .

[11]  Jinde Cao,et al.  Stability analysis for switched genetic regulatory networks: An average dwell time approach , 2011, Journal of the Franklin Institute.

[12]  Jinde Cao,et al.  Global robust point dissipativity of interval neural networks with mixed time-varying delays , 2009 .

[13]  Graziano Chesi,et al.  Robustness analysis of genetic regulatory networks affected by model uncertainty , 2011, Autom..

[14]  Mario di Bernardo,et al.  Analysis, design and implementation of a novel scheme for in-vivo control of synthetic gene regulatory networks , 2011, Autom..

[15]  Jian-Xin Xu,et al.  Nonlinear integral-type sliding surface for both matched and unmatched uncertain systems , 2004, IEEE Transactions on Automatic Control.

[16]  Jun Zhao,et al.  Passivity and stability of switched systems: A multiple storage function method , 2008, Syst. Control. Lett..

[17]  R. Lu,et al.  Passivity analysis of stochastic time-delay neural networks , 2010 .

[18]  Vahid Johari Majd,et al.  Dissipativity-based stable controller redesign for nonlinear MIMO switched systems in the presence of perturbations , 2014 .

[19]  K. Aihara,et al.  Synchronization of coupled nonidentical genetic oscillators , 2006, Physical biology.

[20]  Zidong Wang,et al.  Monostability and multistability of genetic regulatory networks with different types of regulation functions , 2010 .

[21]  Zidong Wang,et al.  Exponential synchronization of complex networks with Markovian jump and mixed delays , 2008 .

[22]  Jinde Cao,et al.  Asymptotic and robust stability of genetic regulatory networks with time-varying delays , 2008, Neurocomputing.

[23]  Edward R. Dougherty,et al.  Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks , 2002, Bioinform..

[24]  P. Swain,et al.  Stochastic Gene Expression in a Single Cell , 2002, Science.

[25]  Vahid Johari Majd,et al.  Robust stability analysis of stochastic genetic regulatory networks with discrete and distributed delay in both mRNA and protein dynamics , 2010, 2010 IEEE Conference on Cybernetics and Intelligent Systems.

[26]  Huijun Gao,et al.  Distributed Synchronization in Networks of Agent Systems With Nonlinearities and Random Switchings , 2013, IEEE Transactions on Cybernetics.

[27]  Huijun Gao,et al.  New Delay-Dependent Exponential Stability for Neural Networks With Time Delay , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[28]  Jean-Luc Gouzé,et al.  A mathematical framework for the control of piecewise-affine models of gene networks , 2008, Autom..

[29]  Zidong Wang,et al.  State estimation for Markov-type genetic regulatory networks with delays and uncertain mode transition rates , 2009 .

[30]  Huijun Gao,et al.  New results on stabilization of Markovian jump systems with time delay , 2009, Autom..

[31]  José Eduardo Ribeiro Cury,et al.  Systems Biology, Synthetic Biology and Control Theory: A promising golden braid , 2013, Annu. Rev. Control..

[32]  K. Aihara,et al.  Stability of genetic regulatory networks with time delay , 2002 .

[33]  Jian-An Fang,et al.  Exponential stability of switched genetic regulatory networks with both stable and unstable subsystems , 2013, J. Frankl. Inst..

[34]  J. Collins,et al.  Construction of a genetic toggle switch in Escherichia coli , 2000, Nature.

[35]  D. Pincus,et al.  In silico feedback for in vivo regulation of a gene expression circuit , 2011, Nature Biotechnology.

[36]  M. Elowitz,et al.  A synthetic oscillatory network of transcriptional regulators , 2000, Nature.

[37]  Lixian Zhang,et al.  Passivity and passification for Markov jump genetic regulatory networks with time-varying delays , 2014, Neurocomputing.

[38]  Ju H. Park,et al.  Robust dissipativity analysis of neural networks with time-varying delay and randomly occurring uncertainties , 2012 .

[39]  Rainer Breitling,et al.  What is Systems Biology? , 2010, Front. Physiology.

[40]  E. O’Shea,et al.  Living with noisy genes: how cells function reliably with inherent variability in gene expression. , 2007, Annual review of biophysics and biomolecular structure.

[41]  Zidong Wang,et al.  Robust stability of discrete-time stochastic neural networks with time-varying delays , 2008, Neurocomputing.

[42]  Hossein Shokouhi-Nejad,et al.  Robust H(∞) observer-based controller for stochastic genetic regulatory networks. , 2014, Mathematical biosciences.