This paper considers the problem of computing the non-causal minimum-fuel energy management strategy of a hybrid electric vehicle on a given driving cycle. Specifically, we address the multiphase mixed-integer nonlinear optimal control problem arising when 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 phase specific right-hand side functions accounting for different powertrain operating modes. Gearbox and driveability requirements translate into combinatorial constraints, which have not been included in previous work, but are part of our algorithmic framework. We devise a tailored algorithm to solve our problem by extending the combinatorial integral approximation technique that breaks down the original mixed-integer nonlinear program into a sequence of nonlinear programs and mixed-integer linear programs and discuss thereafter its approximation error. Finally, we showcase the effectiveness of the proposed methodology in terms of solution quality and reasonable run time by analyzing two case studies.
Robuschi, Nicolò, Zeile, Clemens, Sager, Sebastian, Braghin, Francesco and Cheli, Federico. "Multiphase Mixed-Integer Nonlinear Optimal Control of Hybrid Electric Vehicles", Automatica, accepted.