Game-theoretic Energy Management Strategies With Interacting Agents in Formula 1

This paper presents an interaction-aware energy management optimization framework for Formula 1 racing. The considered scenario involves two agents and a drag reduction model. Strategic interactions between the agents are captured by a Stackelberg game formulated as a bilevel program. To address the computational challenges associated with bilevel optimization, the problem is reformulated as a single-level nonlinear program employing the Karush-Kuhn-Tucker conditions. The proposed framework contributes towards the development of new energy management and allocation strategies, caused by the presence of another agent. For instance, it provides valuable insights on how to redistribute the energy in order to optimally exploit the wake effect, showcasing a notable difference with the behavior studied in previous works. Robust energy allocations can be identified to reduce the lap time loss associated with unexpected choices of the other agent. It allows to recognize the boundary conditions for the interaction to become relevant, impacting the system's behavior, and to assess if overtaking is possible and beneficial. Overall, the framework provides a comprehensive approach for a two-agent Formula 1 racing problem with strategic interactions, offering physically intuitive and practical results.