This paper considers the infinite horizon optimal control of logical control networks, including Boolean control networks as a special case. Using the framework of game theory, the optimal control problem is formulated. In the sight of the algebraic form of a logical control network, its cycles can be calculated algebraically. Then the optimal control is revealed over a certain cycle. When the games, using memory mu > 1 (which means the players only consider previous mu steps' action at each step), are considered, the higher order logical control network is introduced and its algebraic form is also presented, which corresponds to a conventional logical control network (i.e., mu = 1). Then it is proved that the optimization technique developed for conventional logical control networks is also applicable to this mu-memory case.