Two kinds of optimal controls for probabilistic mix-valued logical dynamic networks

This paper addresses two kinds of optimal control problems of probabilistic mix-valued logical control networks by using the semi-tensor product of matrices, and presents a number of new results on the optimal finite-horizon control and the first-passage model based control problems, respectively. Firstly, the probabilistic mix-valued logical control network is expressed in an algebraic form by the semi-tensor product method, based on which the optimal finite-horizon control problem is studied and a new algorithm for choosing a sequence of control actions is established to minimize a given cost functional over finite steps. Secondly, the first-passage model of probabilistic mix-valued logical networks is given and a new algorithm for designing the optimal control scheme is proposed to maximize the corresponding probability criterion. Finally, an illustrative example is studied to support our new results/algorithms.