Feedback stabilization, regulation and optimal control of Boolean control networks

In this paper various control problems for Boolean control networks (BCNs) are investigated. By resorting to some recent results regarding the infinite-horizon optimal control, we first provide an alternative proof of the fact that the stabilization of a BCN to a given reachable equilibrium point can always be performed by means of a static state-feedback. Secondly, upon deriving necessary and sufficient conditions for the solvability of the output regulation problem, we show that, when such conditions are satisfied, also this problem can be solved by means of a static state-feedback. In both cases, a feedback gain matrix is explicitly derived by making use of the results obtained for the optimal control problem. Finally, some preliminary results about the stabilization problem by means of a static, either time-invariant or time-varying, output feedback are also presented.