Real-Time Model Predictive Control for a Parallel Hybrid Electric Vehicle Using Outer Approximation and Semi-Convex Cut Generation**This Work Has Been Carried out Within the Framework of KU Leuven - BOF PFV/10/002 Centre of Excellence: Optimization in Engineering (OPTEC) and DrivetrainCodesign: Flanders Make ICON: Physical and Control Co-Design of Electromechanical Drivetrains for Machines and Vehicles. Flanders Make is the Flemish Strategic Research Centre for the Manufacturing Industry.

Hybrid Electric Vehicles (HEVs) have the potential of yielding better fuel economy and lower emissions compared to their traditional counterparts. This advantage comes with the drawback that drivers are no longer capable of efficiently controlling the power-train of their vehicles. Consequently, good automatic control is crucial for HEV design. In this paper the full development of the power-train control system of a Parallel-HEV is presented. The proposed control approach is Mixed-Integer Model Predictive Control (MI-MPC). A suitable MI-MPC formulation is developed starting from the modeling of the propulsion components of the power-train based on a set of real-world data. After guiding the reader through the development of the model. An innovative solution approach is presented to deal with the inherit non-convexity of the resulting problem formulation. The peculiar form of non-convexity in the model is harnessed in order to develop a variation of the Outer Approximation algorithm capable of efficiently tackling the solution of the mixed-integer optimization problems required by the MI-MPC framework. In conclusion, a numerical experiment will show the real-time applicability of the resulting control system and highlight its limits.