Optimal control of multiagent systems via game theory is investigated. Assuming a system level object is given, the utility functions for individual agents are designed to convert a multiagent system into a potential game. First, for fixed topology (i.e., the network geometric structure), a necessary and sufficient condition is given to ensure the existence of local information based utility functions. Then using local information the system can converge to a maximum point of the system object, which is a Nash equilibrium. It is also proved that a networked evolutionary potential game is a special case of this multiagent system. Second, for time-varying topology, the state based potential game is utilized to design the optimal control. A strategy based Markov state transition process is proposed to ensure the existence of state based potential functions. As an extension of the fixed topology case, a necessary and sufficient condition for the existence of state depending utility functions using local information is also presented. It is also proved that using a better reply with inertia strategy, the system converges to a maximum point of the state based system object, which is called a recurrent state equilibrium.