PMP (Pontryagin's minimum principle) produces only the conditions necessary for an optimal solution. However, it can be sufficient conditions for a global optimal solution when the problem gives us additional information about the system's behaviors. In this paper, we show that the case of the optimal control for HEVs (hybrid electric vehicles) has fulfilled this expectation. When the fuel consumption rate m˙fc is a convex function of Pbat, and the time derivative SO˙C of the SOC (state of charge) is a concave function of Pbat and the SOC, the control idea based on PMP always generates a global optimal solution. We showed that the convexity and the concavity are quite natural characteristics of the control problem for HEVs. On the basis of this conclusion, we can expand the application of the control concept from HEVs to PHEVs (plug-in hybrid electric vehicles), whereas the previous study limited the application of this concept to HEVs that use small ranges of SOCs because the assumption in the study did not guarantee optimality over wide ranges of SOCs. Additionally, we simulated the vehicle with a battery that does not have a concave function for the SO˙C, and the results show that PMP-based control could produce alternative solutions with the unusual battery. In those alternatives, the energy management strategies could be very different even for the same driving cycle. Although PMP control could be a global optimal solution, we cannot determine the optimal co-state without information about future conditions. Nevertheless, the beauty of PMP is that unpredictable and complicated information applicable to future situations could be implied by the co-state, which is the only parameter that we need to consider for optimality. Because the control concept based on PMP already provides an optimized form of control through the Hamiltonian, it is very efficient to archive the optimality (or, at least, it is not easy to fall into inefficient control). Although the problem of connecting future information to the costate still remains unsolved, the PMP control concept should be considered to be a promising solution for problems that need to be addressed in both simulations and the real world.


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    Title :

    Sufficient conditions of optimal control based on Pontryagin's minimum principle for use in hybrid electric vehicles


    Contributors:


    Publication date :

    2012


    Size :

    11 Seiten, 15 Bilder, 2 Tabellen, 27 Quellen




    Type of media :

    Article (Journal)


    Type of material :

    Print


    Language :

    English