Multiphase mixed-integer nonlinear optimal control of hybrid electric vehicles

This study considers the problem of computing a non-causal minimum-fuel energy management strategy for a hybrid electric vehicle on a given driving cycle. Specifically, we address the multiphase mixed-integer nonlinear optimal control problem that arises when the optimal gear choice, torque split and engine on/off controls are sought in off-line evaluations. We propose an efficient model by introducing vanishing constraints and a phase specific right-hand side function that accounts for the different powertrain operating modes. The gearbox and driveability requirements translate into combinatorial constraints. These constraints have not been included in previous research; however, they are part of the algorithmic framework for this investigation. We devise a tailored algorithm to solve this problem by extending the combinatorial integral approximation (CIA) technique that breaks down the original mixed-integer nonlinear program into a sequence of nonlinear programs and mixed-integer linear programs, followed by a discussion of its approximation error. Finally, numerical results illustrate the proposed algorithm in terms of solution quality and run time.