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ORNL researcher proposes solution for online optimization of power management in HEVs/PHEVs and for different drivers

Dr. Andreas Malikopoulos at Oak Ridge National Laboratory (ORNL) has developed a solution for the online optimization of power management in parallel HEVs/PHEVs and for any different driver (i.e., for different driving styles). A paper on his work is published in IEEE Transactions on Control Systems Technology.

There has been a great deal of work done since the late 1990s on the optimization of power management control—i.e., the optimal distribution of power demanded by the driver to the available subsystems of combustion engine, motor, generator and battery—in parallel HEVs. Despite that significant body of work, Malikopoulos notes, deriving online an optimal solution for different driving styles still remains a challenging control problem.

Broadly, Malikopoulos used a three-stage approach:

  1. Developing the analytical formulation for modeling HEV operation as a controlled Markov chain;

  2. Developing a multiobjective optimization framework that can be used to derive the optimal control policy;

  3. Implementing the Pareto control policy that minimizes the long-run expected average cost criterion and the conditions under which this policy exists.

Unlike other approaches to online optimization, Malikopoulos shows the evolution of the HEV state, rather than the driver’s power demand, to be a controlled Markov chain.

Thus, the driver is considered as an unknown disturbance to the system, i.e., the future driver behavior is unknown, and it is assumed that the pedal position, e.g., acceleration or brake, is a sequence of independent random variables, which takes values in a given finite set… Based on this assumption, it can be shown that the evolution of the system is a controlled Markov chain. This allows us to describe the evolution of the state of the system (HEV) by means of the one-step transition probability…

… There are still open issues, however, with practical implications. First, the proposed solution optimizes the efficiency for any driver using the long-run expected average cost criterion. Namely, being able to derive the optimal control policy online for a specific trip (e.g., total cost criterion from point A to point B) still remains an open issue. Second, the proposed solution uses the efficiency maps of the engine and the motor corresponding to their steady-state operation. Although the supervisory controller in HEVs designates the nominal set points for each subsystem for the lower level controllers, the implications of the solution in transient operation need further investigation. One potential approach to address this is to learn the transient operation of the system corresponding to the driver’ driving style and account for it.

—Malikopoulos (2015)

Malikopoulos validated the effectiveness of the efficiency of the Pareto control policy through the simulation of an HEV model for different driving cycles, and compared it with the DP [dynamic programming] control policy using the average cost criterion. Both control policies achieved the same cumulative fuel consumption, demonstrating that the Pareto control policy is an optimal control policy that minimizes the long-run expected average cost criterion, Malikopoulos concluded.

He is extending the work, with the proposed multiobjective optimization framework now considering the battery in the problem formulation in addition to the engine’s fuel consumption and motor’s efficiency.

He intends for this extended optimization framework to enhance the understanding of the associated tradeoffs among the HEV subsystems, e.g., the engine, the motor, and the battery.


  • Malikopoulos, A.A., (2015) “A Multiobjective Optimization Framework for Online Stochastic Optimal Control in Hybrid Electric Vehicles,” in Control Systems Technology, IEEE Transactions on doi: 10.1109/TCST.2015.2454444


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