The invention relates to a system and a method for improving vehicle driveline operation. Provided are methods and systems for operating a hybrid driveline. The hybrid driveline includes an engine andan electric machine are presented. In one non-limiting example, the engine and electric machine are operated according to a solution of a Hamiltonian that includes a first co-state and a second co-state, an engine fuel flow parameter, a rate of change of battery state of charge parameter, and an emissions flow rate parameter.