Convex relaxations in the optimal control of electrified vehicles

Paper in proceeding, 2015

When controlling the energy flow in electrified powertrains by means of convex optimization, the typically non-convex set of the original formulation needs to be relaxed to a convex super-set. In this paper we show that when using the backward simulation approach, where vehicle velocity is equal to the reference velocity, the global optimum of the original non-convex problem can be obtained by solving the relaxed convex problem. When vehicle velocity is kept as a state in the problem, in the so called forward simulation approach, we provide a condition for which, when satisfied, an agreement will be achieved between the solutions of the relaxed and the original problem.