Optimal control of finite-valued networks

Control of finite-valued networks, including Boolean networks, is currently a hot topic. In this paper the optimization control of the networks with present value performance criterion is discussed. The problem is formulated as a finite strategy game between human and machine. It is firstly proved that the optimal strategy can be found in the set of periodic strategies, which makes the problem finitely computable, though the computational complexity of exhaustion might be a severe problem. Then an efficient numerical method is developed to solve the problem. Some interesting examples are presented to demonstrate the efficiency of our results.