{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T00:03:28Z","timestamp":1784678608182,"version":"3.55.0"},"reference-count":51,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Communications in Nonlinear Science and Numerical Simulation"],"published-print":{"date-parts":[[2026,11]]},"DOI":"10.1016\/j.cnsns.2026.110401","type":"journal-article","created":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T23:28:20Z","timestamp":1781911700000},"page":"110401","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"P3","title":["Stabilization of Boolean control networks with probabilistic state-dependent control constraints via induced equations"],"prefix":"10.1016","volume":"162","author":[{"given":"Zifan","family":"Huang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xingyu","family":"Ge","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenbo","family":"Qi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7196-5753","authenticated-orcid":false,"given":"Jie","family":"Zhong","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yanling","family":"Zheng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiangyong","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"3","key":"10.1016\/j.cnsns.2026.110401_bib0001","doi-asserted-by":"crossref","first-page":"336","DOI":"10.1093\/bioinformatics\/btl596","article-title":"Qualitatively modelling and analysing genetic regulatory networks: a Petri net approach","volume":"23","author":"Steggles","year":"2007","journal-title":"Bioinformatics"},{"issue":"3","key":"10.1016\/j.cnsns.2026.110401_bib0002","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1006402","article-title":"Boolean model of growth signaling, cell cycle and apoptosis predicts the molecular mechanism of aberrant cell cycle progression driven by hyperactive PI3K","volume":"15","author":"Sizek","year":"2019","journal-title":"PLoS Comput Biol"},{"key":"10.1016\/j.cnsns.2026.110401_bib0003","series-title":"International conference on computational methods in systems biology","first-page":"57","article-title":"Abduction based drug target discovery using Boolean control network","author":"Biane","year":"2017"},{"issue":"4","key":"10.1016\/j.cnsns.2026.110401_bib0004","doi-asserted-by":"crossref","first-page":"670","DOI":"10.1016\/j.jtbi.2006.09.023","article-title":"Control of Boolean networks: hardness results and algorithms for tree structured networks","volume":"244","author":"Akutsu","year":"2007","journal-title":"J Theor Biol"},{"key":"10.1016\/j.cnsns.2026.110401_bib0005","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1016\/j.mbs.2018.09.009","article-title":"Stochastic hybrid models of gene regulatory networks\u2013a pde approach","volume":"305","author":"Kurasov","year":"2018","journal-title":"Math Biosci"},{"issue":"5","key":"10.1016\/j.cnsns.2026.110401_bib0006","doi-asserted-by":"crossref","first-page":"1211","DOI":"10.1109\/TCBB.2024.3378155","article-title":"Network modeling and control of dynamic disease pathways, review and perspectives","volume":"21","author":"Hsiao","year":"2024","journal-title":"IEEE\/ACM Trans Comput Biol Bioinf"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110401_bib0007","doi-asserted-by":"crossref","first-page":"15","DOI":"10.4236\/jbise.2008.11003","article-title":"Construction and control of genetic regulatory networks: a multivariate markov chain approach","volume":"1","author":"Zhang","year":"2008","journal-title":"J Biomed Sci Eng"},{"issue":"3","key":"10.1016\/j.cnsns.2026.110401_bib0008","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1016\/0022-5193(69)90015-0","article-title":"Metabolic stability and epigenesis in randomly constructed genetic nets","volume":"22","author":"Kauffman","year":"1969","journal-title":"J Theor Biol"},{"issue":"4","key":"10.1016\/j.cnsns.2026.110401_bib0009","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.93.048701","article-title":"Activities and sensitivities in Boolean network models","volume":"93","author":"Shmulevich","year":"2004","journal-title":"Phys Rev Lett"},{"key":"10.1016\/j.cnsns.2026.110401_bib0010","series-title":"Analysis and control of Boolean networks: a semi-tensor product approach","author":"Cheng","year":"2010"},{"issue":"9","key":"10.1016\/j.cnsns.2026.110401_bib0011","doi-asserted-by":"crossref","first-page":"17448","DOI":"10.1109\/TNNLS.2025.3559207","article-title":"Robust controllability of Boolean control networks via dynamic programming","volume":"36","author":"Li","year":"2025","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"issue":"20","key":"10.1016\/j.cnsns.2026.110401_bib0012","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11071-025-11575-5","article-title":"Controllability of switched Boolean networks with constraints by dynamic logic-based switching","volume":"113","author":"Tu","year":"2025","journal-title":"Nonlinear Dyn"},{"issue":"6","key":"10.1016\/j.cnsns.2026.110401_bib0013","doi-asserted-by":"crossref","first-page":"1218","DOI":"10.1016\/j.automatica.2012.03.022","article-title":"Controllability of Boolean control networks via the Perron\u2013Frobenius theory","volume":"48","author":"Laschov","year":"2012","journal-title":"Automatica"},{"issue":"3","key":"10.1016\/j.cnsns.2026.110401_bib0014","doi-asserted-by":"crossref","DOI":"10.1007\/s11432-015-5369-8","article-title":"Controllability of Boolean control networks with state-dependent constraints","volume":"59","author":"Guo","year":"2016","journal-title":"Sci China Inf Sci"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110401_bib0015","doi-asserted-by":"crossref","first-page":"1374","DOI":"10.1109\/TNSE.2023.3322567","article-title":"Observability categorization for Boolean control networks","volume":"11","author":"Lin","year":"2024","journal-title":"IEEE Trans Netw Sci Eng"},{"issue":"10","key":"10.1016\/j.cnsns.2026.110401_bib0016","doi-asserted-by":"crossref","first-page":"7028","DOI":"10.1109\/TAC.2024.3389822","article-title":"Improved criteria for controllability of Markovian jump Boolean control networks with time-varying state delays","volume":"69","author":"Tang","year":"2024","journal-title":"IEEE Trans Autom Control"},{"key":"10.1016\/j.cnsns.2026.110401_bib0017","doi-asserted-by":"crossref","DOI":"10.1016\/j.cnsns.2023.107653","article-title":"Controllability of generalized asynchronous Boolean networks with periodical impulsive control","volume":"128","author":"Su","year":"2024","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"4","key":"10.1016\/j.cnsns.2026.110401_bib0018","doi-asserted-by":"crossref","first-page":"140207:1","DOI":"10.1007\/s11432-025-4750-x","article-title":"Observability and approximate observability of Boolean control networks from finite offline data","volume":"69","author":"Ge","year":"2026","journal-title":"Sci China Inf Sci"},{"issue":"3","key":"10.1016\/j.cnsns.2026.110401_bib0019","doi-asserted-by":"crossref","first-page":"3291","DOI":"10.1002\/mma.10485","article-title":"Minimal observability of switching Boolean networks","volume":"48","author":"Sun","year":"2025","journal-title":"Math Methods Appl Sci"},{"issue":"8","key":"10.1016\/j.cnsns.2026.110401_bib0020","doi-asserted-by":"crossref","first-page":"4273","DOI":"10.1109\/TCSI.2025.3553463","article-title":"Observability verification system analysis for observability and reconstructibility of probabilistic logical control networks","volume":"72","author":"Li","year":"2025","journal-title":"IEEE Trans Circuits Syst I Regul Pap"},{"issue":"7","key":"10.1016\/j.cnsns.2026.110401_bib0021","doi-asserted-by":"crossref","first-page":"1031","DOI":"10.1049\/iet-cta.2018.5279","article-title":"Observability of Boolean networks via STP and graph methods","volume":"13","author":"Liu","year":"2019","journal-title":"IET Control Theory Appl"},{"key":"10.1016\/j.cnsns.2026.110401_bib0022","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/j.cnsns.2017.07.001","article-title":"Cluster synchronization of Boolean network","volume":"55","author":"Zhang","year":"2018","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110401_bib0023","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1109\/LCSYS.2020.3001993","article-title":"Reinforcement learning approach to feedback stabilization problem of probabilistic Boolean control networks","volume":"5","author":"Acernese","year":"2021","journal-title":"IEEE Control Syst Lett"},{"issue":"9","key":"10.1016\/j.cnsns.2026.110401_bib0024","doi-asserted-by":"crossref","first-page":"6242","DOI":"10.1109\/TSMC.2025.3578029","article-title":"Link augmentation and Q-learning for set stabilization in switched Boolean networks","volume":"55","author":"Pan","year":"2025","journal-title":"IEEE Trans Syst Man Cybern Syst"},{"key":"10.1016\/j.cnsns.2026.110401_bib0025","article-title":"Local stabilization of Boolean control networks via stochastic sampled-data control","volume":"511","author":"Chen","year":"2026","journal-title":"Appl Math Comput"},{"key":"10.1016\/j.cnsns.2026.110401_bib0026","doi-asserted-by":"crossref","DOI":"10.1016\/j.cnsns.2026.109662","article-title":"Output feedback state estimation for weakly reconstructible Boolean control networks","volume":"156","author":"Yang","year":"2026","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"6","key":"10.1016\/j.cnsns.2026.110401_bib0027","doi-asserted-by":"crossref","first-page":"4393","DOI":"10.1109\/TNSE.2022.3201039","article-title":"Stabilization of logical dynamic networks via event-triggered switching signals and its application","volume":"9","author":"Ding","year":"2022","journal-title":"IEEE Trans Netw Sci Eng"},{"issue":"6","key":"10.1016\/j.cnsns.2026.110401_bib0028","doi-asserted-by":"crossref","first-page":"4345","DOI":"10.1109\/TNSE.2025.3555801","article-title":"A method to stabilize large-scale Boolean networks via pinning control","volume":"12","author":"Liu","year":"2025","journal-title":"IEEE Trans Netw Sci Eng"},{"issue":"3","key":"10.1016\/j.cnsns.2026.110401_bib0029","doi-asserted-by":"crossref","first-page":"1818","DOI":"10.1109\/TNSE.2025.3539878","article-title":"A graphical approach for robust set stabilization of Boolean control networks with lowest time complexity","volume":"12","author":"Li","year":"2025","journal-title":"IEEE Trans Netw Sci Eng"},{"key":"10.1016\/j.cnsns.2026.110401_bib0030","article-title":"Robust stabilization of asynchronous probabilistic Boolean control networks subject to one-bit perturbations","volume":"152","author":"Wang","year":"2025","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"10.1016\/j.cnsns.2026.110401_bib0031","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.automatica.2017.06.040","article-title":"On algorithms for state feedback stabilization of Boolean control networks","volume":"84","author":"Liang","year":"2017","journal-title":"Automatica"},{"issue":"3","key":"10.1016\/j.cnsns.2026.110401_bib0032","doi-asserted-by":"crossref","DOI":"10.1007\/s11432-021-3430-7","article-title":"Asymptotical stability of continuous-time probabilistic logic networks based on transition rate","volume":"66","author":"Li","year":"2023","journal-title":"Sci China Inf Sci"},{"issue":"9","key":"10.1016\/j.cnsns.2026.110401_bib0033","doi-asserted-by":"crossref","first-page":"4623","DOI":"10.1109\/TCYB.2020.3003055","article-title":"Perturbation analysis for finite-time stability and stabilization of probabilistic Boolean networks","volume":"51","author":"Li","year":"2021","journal-title":"IEEE Trans Cybern"},{"issue":"10","key":"10.1016\/j.cnsns.2026.110401_bib0034","doi-asserted-by":"crossref","first-page":"7211","DOI":"10.1109\/TAC.2024.3394549","article-title":"Stability analysis of block logical dynamical systems and its application in logical networks with time delay","volume":"69","author":"Li","year":"2024","journal-title":"IEEE Trans Autom Control"},{"issue":"2","key":"10.1016\/j.cnsns.2026.110401_bib0035","doi-asserted-by":"crossref","first-page":"1198","DOI":"10.1109\/TSMC.2022.3195196","article-title":"Reachability, controllability, and stabilization of Boolean control networks with stochastic function perturbations","volume":"53","author":"Yang","year":"2023","journal-title":"IEEE Trans Syst Man Cybern Syst"},{"issue":"7","key":"10.1016\/j.cnsns.2026.110401_bib0036","doi-asserted-by":"crossref","first-page":"1978","DOI":"10.1109\/TAC.2014.2298731","article-title":"Stability analysis for switched Boolean networks under arbitrary switching signals","volume":"59","author":"Li","year":"2014","journal-title":"IEEE Trans Autom Control"},{"key":"10.1016\/j.cnsns.2026.110401_bib0037","doi-asserted-by":"crossref","DOI":"10.1016\/j.automatica.2019.108768","article-title":"Set stability of switched delayed logical networks with application to finite-field consensus","volume":"113","author":"Li","year":"2020","journal-title":"Automatica"},{"issue":"7","key":"10.1016\/j.cnsns.2026.110401_bib0038","first-page":"2553","article-title":"Stabilization of delayed Boolean control networks with state constraints: a barrier Lyapunov function method","volume":"68","author":"Liu","year":"2021","journal-title":"IEEE Trans Circuits Syst II Express Br"},{"key":"10.1016\/j.cnsns.2026.110401_bib0039","doi-asserted-by":"crossref","DOI":"10.1016\/j.cnsns.2025.108710","article-title":"Event-triggered output feedback stabilization of Boolean control networks via Ledley solution","volume":"145","author":"Feng","year":"2025","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"7","key":"10.1016\/j.cnsns.2026.110401_bib0040","doi-asserted-by":"crossref","first-page":"1853","DOI":"10.1109\/TAC.2013.2238092","article-title":"State feedback stabilization for Boolean control networks","volume":"58","author":"Li","year":"2013","journal-title":"IEEE Trans Autom Control"},{"issue":"4","key":"10.1016\/j.cnsns.2026.110401_bib0041","doi-asserted-by":"crossref","first-page":"2206","DOI":"10.1109\/TCYB.2022.3219522","article-title":"State estimation via designing controller and state estimation-based stabilization for Boolean control networks","volume":"54","author":"Chen","year":"2024","journal-title":"IEEE Trans Cybern"},{"issue":"4","key":"10.1016\/j.cnsns.2026.110401_bib0042","doi-asserted-by":"crossref","first-page":"1882","DOI":"10.1109\/TCNS.2020.3007820","article-title":"Redefined reconstructibility and state estimation for Boolean networks","volume":"7","author":"Yang","year":"2020","journal-title":"IEEE Trans Control Netw Syst"},{"issue":"8","key":"10.1016\/j.cnsns.2026.110401_bib0043","first-page":"3565","article-title":"Stability and pinning stabilization of Markovian jump Boolean networks","volume":"69","author":"Meng","year":"2022","journal-title":"IEEE Trans Circuits Syst II Express Br"},{"issue":"11","key":"10.1016\/j.cnsns.2026.110401_bib0044","doi-asserted-by":"crossref","first-page":"4524","DOI":"10.1109\/TNNLS.2019.2955974","article-title":"Asymptotical feedback set stabilization of probabilistic Boolean control networks","volume":"31","author":"Zhou","year":"2020","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110401_bib0045","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1109\/TNSE.2022.3208335","article-title":"Necessary and sufficient conditions for security of hidden Markov Boolean control networks under shifting attacks","volume":"10","author":"Wang","year":"2023","journal-title":"IEEE Trans Netw Sci Eng"},{"issue":"10","key":"10.1016\/j.cnsns.2026.110401_bib0046","doi-asserted-by":"crossref","first-page":"4820","DOI":"10.1109\/TAC.2020.3037142","article-title":"Induced-equations-based stability analysis and stabilization of Markovian jump Boolean networks","volume":"66","author":"Zhu","year":"2021","journal-title":"IEEE Trans Autom Control"},{"issue":"4","key":"10.1016\/j.cnsns.2026.110401_bib0047","doi-asserted-by":"crossref","first-page":"1779","DOI":"10.1109\/TAC.2019.2934532","article-title":"Asymptotical stability of probabilistic Boolean networks with state delays","volume":"65","author":"Zhu","year":"2020","journal-title":"IEEE Trans Autom Control"},{"issue":"5","key":"10.1016\/j.cnsns.2026.110401_bib0048","doi-asserted-by":"crossref","first-page":"2955","DOI":"10.1137\/120902331","article-title":"Controllability analysis and control design for switched Boolean networks with state and input constraints","volume":"53","author":"Li","year":"2015","journal-title":"SIAM J Control Optim"},{"key":"10.1016\/j.cnsns.2026.110401_bib0049","doi-asserted-by":"crossref","unstructured":"Boutilier C., Cohen A., Daniely A., Hassidim A., Mansour Y., Meshi O., et al. Planning and learning with stochastic action sets. 2018; arXiv preprint arXiv: 180502363.","DOI":"10.24963\/ijcai.2018\/650"},{"key":"10.1016\/j.cnsns.2026.110401_bib0050","series-title":"Markov chains and stochastic stability","author":"Meyn","year":"2012"},{"key":"10.1016\/j.cnsns.2026.110401_bib0051","series-title":"Mathematical concepts and methods in modern biology: using modern discrete models","author":"Robeva","year":"2013"}],"container-title":["Communications in Nonlinear Science and Numerical Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1007570426007550?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1007570426007550?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T23:33:53Z","timestamp":1784676833000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1007570426007550"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,11]]},"references-count":51,"alternative-id":["S1007570426007550"],"URL":"https:\/\/doi.org\/10.1016\/j.cnsns.2026.110401","relation":{},"ISSN":["1007-5704"],"issn-type":[{"value":"1007-5704","type":"print"}],"subject":[],"published":{"date-parts":[[2026,11]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Stabilization of Boolean control networks with probabilistic state-dependent control constraints via induced equations","name":"articletitle","label":"Article Title"},{"value":"Communications in Nonlinear Science and Numerical Simulation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cnsns.2026.110401","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"110401"}}