Explicit solutions for optimal control of electric and automated buses in urban lines

The rapid spread of electric and automated buses in cities offers great benefits in terms of both environmental impact and safety, but it also requires a rethinking of the control policies adopted to ensure public transport. Indeed, the need to control bus speed to meet schedules along with the need to take decisions related to battery charging lead to the formalization of multi-objective control problems such as the one proposed in this paper. However, solving a multi-objective problem can be challenging or impractical in the real-world implementations. The goal of this paper is to identify explicit solutions that can be applied when certain operating conditions occur, thus reducing the computational burden at runtime. In addition, a control algorithm is proposed to integrate the application of the explicit solutions with those obtained by solving a multi-objective control problem. The paper concludes with an application to a real case study to demonstrate the effectiveness of the proposed control scheme.