#### A Minimax Framework for Two-Agent Scheduling with Inertial Constraints

##### Feihong Yang, Yuan Shen

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.

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