Optimal power dispatch from battery and engine of a hybrid vehicle through multiparametric mixed-integer programming

Optimal control of hybrid vehicles involving a battery and a combustion engine is necessary for efficient energy management, and this optimal control problem (OCP) can be formulated as a mixed-integer program (MIP). The real-time deployment of MIPs is challenging due to their computational complexity. As the number of integer variables increases, the solution space increases exponentially, requiring computationally expensive methods to solve. Although machine learning-based strategies help reduce computation time, they provide approximate, but not exact, solutions to MIPs and may even involve expensive one-time training, employing heavy computational resources. In this work, a multiparametric (mp) programming framework is used to improve the computation time of an OCP for hybrid vehicles while getting the exact solution; furthermore, the mp-programming framework allows for implementation through low-cost hardware like a chip without needing a computer. In the mp-programming approach, the solution is expressed as a set of piecewise linear functions in terms of the uncertain parameters that change with time. During online calculations, the optimal solution is determined through a point location search procedure. This framework is compared with the state-of-the-art branch-and-bound method in the Gurobi solver and a neural network solver model developed in this work.