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

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.