Realization of pmp-based control for hybrid electric vehicles in a backward-looking simulation

Optimal control is generally not possible without information about the future coming up, and it is not easy to obtain an optimal solution even though the information is given a priori. In this paper, a control concept based on Pontryagin’s Minimum Principle (PMP) is introduced as an efficient solution to generate an optimal control trajectory for Hybrid Electric Vehicles (HVEs) when the performance of the vehicles is evaluated on scheduled driving cycles at a simulation level. The main idea of the control concept is to minimize Hamiltonian, which is interpreted as equivalent fuel consumption, and the Hamiltonian is characterized by a co-state, which is interpreted as a weighting factor for the electrical usage. A key aspect of the control problem is that an appropriate initial condition of the co-state is required to satisfy the boundary condition of the problem. In this study, techniques to calculate the Hamiltonian in different hybrid configurations are introduced, and a methodology to look for the initial condition of the co-state is studied, so that the controller is able to realize a desired State Of Charge (SOC) trajectory. To address the issue, we utilize a shooting method with multiple initial conditions based on the concept of the Newton-Raphson method, and all these techniques are realized in a backward looking simulator. The simulation results show that the PMP-based control is a very efficient approach to produce the optimal control trajectory, and the performance is compared to the optimal solution solved by Dynamic Programming (DP).