determination of the equivalent consumption in hybrid electric vehicles in the state-constrained case

In the optimization of power management of hybrid electric vehicles, the equivalent consumption factor is often used. This parameter represents a way of penalizing the use of power from the batteries, taking into account the fuel consumption that such use eventually hides. If the problem of determining the power split between the energy sources of the vehicle that minimizes fuel consumption is stated as a non linear constrained optimal control problem, and is solved using Pontryagin Maximum Principle (PMP), the equivalent consumption factor may be computed from the adjoint state. Following this approach we compute the trajectory of the adjoint state in the case where state constraints are taken into account. The optimality conditions from PMP are a Boundary Value Problem (BVP), which is solved numerically using a code named PASVA4. Numerical examples are compared with dynamic programming solutions of the same problem. It is found that the adjoint state is continuous and its trajectory is described. The approach may be generalized to similar optimal control problems.