A Minimax Framework for Two-Agent Scheduling With Inertial Constraints

Multi-agent scheduling problems are common in applications such as intelligent transportation and smart manufacturing. When the agents are non-cooperative and inertially constrained, finding a safe and efficient policy under the trajectory uncertainty of other agents is a non-trivial problem. In this article, we establish a minimax framework to optimize the worst-case scheduling performance under the two-agent model. Specifically, a unified representation is proposed to characterize the trajectory uncertainty of the other agent, and a function is derived to evaluate different target states. Based on this evaluation, we further develop a control policy by adopting the minimax method, where a trajectory leading to the most robust target state is generated at each step. Algorithms are also provided to ensure the computational tractability of the policy. Furthermore, the safety of the policy is proved, and the global robustness is verified by numerical simulations, which show that the proposed policy reduces the worst-case scheduling cost by 13.1% compared with heuristic policies.