Energy management of hybrid vehicles with state constraints: A penalty and implicit Hamiltonian minimization approach

Abstract

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Economic Nonlinear Predictive Control for Real-Time Optimal Energy Management of Parallel Hybrid Electric Vehicles

“…The application of an on-line adaptation law for equivalence factor reduces the computational burden and guarantees optimality, as described in [21]. An effective penalty method using implicit Hamiltonian minimization is proposed in [22] to deal with problems involving state and input constraints. In [23], the driving cycle of a plug-in hybrid electric bus was divided into several segments based on each bus stop.…”

“…The presented method is adopted from the results in [45] with modifications in the adaptation law for updating the co-state variable s and selecting varying parameters of the battery power-loss coefficient α, the engine efficiency e, and the friction loss of engine P 0 . When there are no constraints of motor and engine in the optimal control problem (22), the Hamiltonian is expressed as a piecewise function of motor power: where…”

“…The purpose of the nonlinear predictive control problem is to optimize fuel efficiency, which is the goal of the original optimal control problem, as well as to maintain battery SOC properly. Therefore, the hard constraint in (22) was converted into a soft constraint by using the battery charge sustaining parameter q δ(i|k) . As a weight for the proper adaptation of the fuel usage and battery usage, the battery charge sustaining parameter was multiplied by the battery usage.…”

“…The unit of fuel and battery usage is J or kWh, and the unit for NO x and HC usage is g. Therefore, in order to unify the meaning of multi-objective for NMPC, q NOx and q HC were multiplied by the NO x or HC usage. The model predictive control problem reformulating the optimal control problem given in (22) is expressed in (25). 1|k)) and the constraint on the battery current (17) and (19) is omitted because the operating limits on the battery power are precisely the same as the operating limits on the battery current.…”

Development of an Efficient Thermal Electric Skipping Strategy for the Management of a Series/Parallel Hybrid Powertrain

“…The aim is to increase the Hamiltonian value whenever the optimal trajectory violates its constraints. An effective penalty approach through an implicit Hamiltonian minimization is employed in [9] with several states and inputs under mixed input-state constraint.…”