A Comparative Study of Supervisory Control Strategies for Hybrid Electric Vehicles

Abstract

Hybrid Electric Vehicles (HEVs) improvements in fuel economy and emissions strongly depend on the energy management strategy. Big obstacles to the control design are the model complexity and the necessity of “a priori” knowledge of torque and velocity profiles for optimal torque split. This paper presents and compares four different energy management approaches for the control of a parallel hybrid electric sport-utility-vehicle.

A Multiobjective Optimization Framework for Online Stochastic Optimal Control in Hybrid Electric Vehicles

“…The Pareto control policy was evaluated over eight driving cycles, and the effectiveness of its efficiency was compared with the DP control policy corresponding to the longrun average cost per unit time optimization criterion (13). The DP control policy was derived though simulation using (14).…”

“…In all the cases, the control policy is derived offline and is optimal either for specific driving cycles or a family of them. Some online approaches [10]- [13], on the other hand, address this problem through an instantaneous optimization problem. The main aspects of these algorithms are concerned with the self-sustainability of the electrical path, which must be guaranteed for the entire driving cycle.…”

“…To solve (13), we need to know the cost function k(X t (1:2) = i, U t (1:2) = μ(X t (1:2) )) or k(i, μ(i )) for simplicity and the transition probabilities P(X t +1(1:2) = j |X t (1:2) = i, U t (1:2) ) of the HEV which are not available a priori. However, we can simulate the HEV model because the state space and control space are known.…”

“…Thus, at each stage t and for a given state X t (1:2) = i ∈ S, the controller can select a control action U t (1:2) = μ(i ), and based on the uncertainty W t (1:2) , the system will transit to a new state X t +1(1:2) = j ∈ S as imposed by the system's dynamics (1), and thus generate a corresponding transition cost k(i, μ(i )). It is then possible to use repeated simulation to calculate (at least approximately) the transition probabilities of the system and the expected one-stage costs by averaging, and then solve the |S| linear equations (13). However, for large and complex systems, e.g., HEVs, a more attractive method to derive the optimal control policy is to learn the optimal control policy rather than explicitly estimating the transition probabilities and stage costs using the Q-learning method.…”

“…Musardo et al [12] presented an adaptive ECMS (A-ECMS) algorithm that periodically computes the equivalence factor and refreshes the control parameters based on the current driving conditions to maximize fuel economy in a parallel HEV. Pisu and Rizzoni [13] compared three algorithms that can be implemented online: a rule-based algorithm, an A-ECMS, and an H ∞ control. The simulation results showed that A-ECMS promises superior robustness and drivability, while it achieves better fuel economy results compared with the rule-based and H ∞ control algorithms.…”