A minimum-time control for Boolean control networks with impulsive disturbances

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• 作者：Hongwei Chen^a ; ^b ; Bo Wu ; ^a ; ^c ; ^{wubo_502@163.com" class="auth_mail" title="E-mail the corresponding author} ; Jianquan Lu^b
• 关键词：Optimal control ; Boolean control network ; Impulsive disturbance ; Semi-tensor product
• 刊名：Applied Mathematics and Computation
• 出版年：2016
• 出版时间：15 January 2016
• 年：2016
• 卷：273
• 期：Complete
• 页码：477-483
• 全文大小：318 K

文摘

This paper investigates a Mayer-type optimal control and minimum-time control of a Boolean control network (BCN) with impulsive disturbances. Using the semi-tensor product, the BCN with impulsive disturbances is converted into algebraic discrete-time impulsive dynamic systems, and several necessary conditions for optimality are derived. Then we consider the problem of steering a BCN with impulsive disturbances from a given initial state to a desired state in minimal time. And a necessary condition, stated in the form of maximum principle, is obtained for a control to be time-optimal. It shows that the impulsive disturbances play an important role in the optimal control problem for BCNs. At last, a biological example is given to illustrate the effectiveness and advantage of the obtained results.