Approximate and approximate null-controllability of a class of piecewise linear Markov switch systems

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• 作者：Dan Goreac^a ; ^{Dan.Goreac@u-pem.fr" class="auth_mail" title="E-mail the corresponding author} ; Alexandra Claudia Grosu^b ; Eduard-Paul Rotenstein^b
• 关键词：Approximate (null-)controllability ; Controlled Markov switch process ; Invariance ; Stochastic gene networks
• 刊名：Systems & Control Letters
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：96
• 期：Complete
• 页码：118-123
• 全文大小：439 K

文摘

We propose an explicit, easily-computable algebraic criterion for approximate null-controllability of a class of general piecewise linear switch systems with multiplicative noise. This gives an answer to the general problem left open in Goreac and Martinez (2015). The proof relies on recent results in Confortola et al. (2015) allowing to reduce the dual stochastic backward system to a family of ordinary differential equations. Second, we prove by examples that the notion of approximate controllability is strictly stronger than approximate null-controllability. A sufficient criterion for this stronger notion is also provided. The results are illustrated on a model derived from repressed bacterium operon (given in Krishna et al. (2005) and reduced in Crudu et al. (2009)).