On the impact of model simplification in input constrained optimal control: Application to HEV energy-thermal management

In this paper, we propose a result allowing to simplify the statement of input constrained optimal control problems. In details, it is shown that perturbation terms of magnitude ε appearing in the dynamics and the cost function can be neglected, because they only yield an improvement of magnitude ε² in the optimal cost. This result, which is is handy for practical applications, is here proven by means of an interior penalty method to deal with input constraints. For illustration, an example of energy management system for a Hybrid Electric Vehicle (HEV) is treated. As is expected, the complexity of the problem can be reduced at very little expense of sub-optimality. Based on simulations, quantitative results in term of fuel consumption are provided.