Determination of the adjoint state evolution for the efficient operation of a hybrid electric vehicle

To minimize fuel consumption in hybrid electric vehicles it is necessary to define a strategy for the management of the power flows within the vehicle. Under the assumption that the velocity to be developed by the vehicle is known a priori, this problem may be posed as a non linear optimal control problem with control and state constraints. We find the solution to this problem using the optimality conditions given by Pontryagin Maximum Principle. This leads to boundary value problems that we solve using a software tool named PASVA4. On real time operation, the velocity to be developed by the vehicle is not known in advance. We show how the adjoint state obtained from the former problem may be used as a weighing factor, called “equivalent consumption”. This weighing factor may be used to design suboptimal real time algorithms for power management.