Optimal finite-horizon control problem of context-sensitive probabilistic Boolean networks with perturbation

This paper investigates the optimal finite-horizon control problem of context-sensitive probabilistic Boolean control networks with perturbation by using the semi-tensor product of matrices, and presents a number of new results/algorithm. Firstly, the context-sensitive probabilistic Boolean network with perturbation is expressed in an algebraical form, and the transition matrix is given by three parts: the general part, the switched part and the perturbation part. Secondly, the optimal finite-horizon control problem is studied and a new algorithm is established to choose a sequence of control actions to minimize a given cost functional over finite steps. Finally, the study of an illustrative example shows that the results/algorithm presented in this paper are very effective.