Powertrain system

A control device of a powertrain system executes a control input determination processing and a system control processing. The control input determination processing includes a co-state variable determination processing to update a co-state variable p of an optimization problem for each time step and a control input calculation processing. The co-state variable determination processing includes an initial value determination processing that determines, as an initial value of the co-state variable p, the sum of a base value of the initial value and an external charge/discharge correction value. The base value is a final value or an average value of the co-state variable p during the last control time period. The external charge/discharge correction value is determined based on an external charge/discharge amount obtained by subtracting a SOC at the end of the last control time period from the SOC at the start of the current control time period.