  Autonomous agents are promising in applications such as intelligent
transportation and smart manufacturing, and scheduling of agents has to take
their inertial constraints into consideration. Most current researches require
the obedience of all agents, which is hard to achieve in non-dedicated systems
such as traffic intersections. In this article, we establish a minimax
framework for the scheduling of two inertially constrained agents with no
cooperation assumptions. Specifically, we first provide a unified and
sufficient representation for various types of situation information, and
define a state value function characterizing the agent's preference of states
under a given situation. Then, the minimax control policy along with the
calculation methods is proposed which optimizes the worst-case state value
function at each step, and the safety guarantee of the policy is also
presented. Furthermore, several generalizations are introduced on the
applicable scenarios of the proposed framework. Numerical simulations show that
the minimax control policy can reduce the largest scheduling cost by $13.4\%$
compared with queueing and following policies. Finally, the effects of decision
period, observation period and inertial constraints are also numerically
discussed.
