Optimal Control Problem of Boolean Control Networks: A Graph-theoretical Approach

Two kinds of optimal control problems of Boolean control networks are investigated in this paper. For these two optimal control problems, existences of optimal control sequences are proved firstly. To find the optimal control sequences, weighted directed graphs are built. Then graph-theoretical approaches are proposed based on the Dijkstra's algorithm for the shortest path problem. Finally, an example is given to show the feasibility of the proposed approaches.