###### Contents
Thus, the concept of the equivalent consumption minimization strategy (ECMS) was developed. In ECMS, the cost of using the stored energy in the battery is weighed against the cost of using fuel with an introduced \"equivalence factor\". Hereafter, real-time strategies that are based upon the observations obtained with [PERSON]'s minimum principle are further developed. The real-time control of plug-in hybrids is more involved in the sense that a depleting strategy is required, such that a constant state-of-energy reference does not work. Real-time strategies that use predictive information, coming from an on-board navigation system, to enhance optimality represent a research topic that has attracted attention as well. Taking everything into account, a logical classification of HEV control strategies is rule-based and optimization-based strategies [8; 9; 10]. On the one hand, it can be concluded that rule-based strategies can be easily implemented in real controllers and their rules can be determined based on human intelligence, heuristics or mathematical models. On the other hand, global optimum solutions can be obtained by performing optimization over a predefined driving cycle. However, this means that it is not possible to perform real-time energy management. In any case, the results of these optimum solutions can be used to benchmark other control strategies and as a basis to define rules for onlineimplementation. The cited online implementation results in the definition of new sub-categories inside the optimization-based control strategies: offline and online strategies. Offline techniques require knowledge of the entire driving cycle. As mentioned before, they can be seen as a good analysis, design and assessment tool for other types of strategies. However, due to their computational complexity, they are not directly implementable for real-time operation. In this category, the following strategies can be highlighted: linear programming (LP), dynamic programming (DP) and metaheuristic search methods. LP solves the problem of fuel consumption optimization by approximating a convex nonlinear optimization problem with a linear programming method. Its problem is that the approximate formulation restricts its application to simple series HEV architectures. DP uses a numerical or analytical model to compute the optimal control strategy to achieve the best fuel consumption. It is able to deal with nonlinearity to find the global optimal solution. Finally, metaheuristic search methods solve optimization problems using stochastic search techniques that reproduce natural processes (e.g., genetic algorithms, particle swarm optimization and simulated annealing). They are effective to solve complex optimization problems with nonlinear, multimodal and non-convex objective functions. All of these offline optimization strategies cannot be used in real-time applications but can provide a benchmark for design and comparison. Online strategies are used when real-time analysis is required. In these strategies, the global criterion of global optimization techniques has to be reduced to an instantaneous optimization. It is achieved by introducing a cost function that only depends on the present state of the system parameters. The following strategies are included in this category: equivalent consumption minimization strategy (ECMS) and model predictive control (MPC). In ECMS, an equivalent fuel factor is calculated that is the actual fuel consumption that is required to recharge the batteries and to recover the energy of the regenerative braking. Then, the total equivalent fuel consumption is the sum of the real fuel consumption of the internal combustion engine (ICE) and the equivalent fuel consumption of the electric motor. Based on this total equivalent fuel consumption, an instantaneous cost function can be calculated and minimized without the necessity for future predictions. The disadvantage of this strategy is that it does not guarantee charge sustainability.