This paper presents a formalization of the energy management problem in hybrid electric vehicles and a comparison of three known methods for solving the resulting optimization problem. Dynamic programming (DP), Pontryagin’s minimum principle (PMP), and equivalent consumption minimization strategy (ECMS) are described and analyzed, showing formally their substantial equivalence. Simulation results are also provided to demonstrate the application of the strategies. The theoretical background for each strategy is described in detail using the same formal framework. Of the three strategies, ECMS is the only implementable in real time; the equivalence with PMP and DP justifies its use as an optimal strategy and allows to tune it more effectively.

1.
Sciarretta
,
A.
, and
Guzzella
,
L.
, 2007, “
Control of Hybrid Electric Vehicles
,”
IEEE Control Syst. Mag.
0272-1708,
27
(
2
), pp.
60
70
.
2.
Serrao
,
L.
,
Onori
,
S.
,
Rizzoni
,
G.
, and
Guezennec
,
Y.
, 2009, “
A Novel Model-Based Algorithm for Battery Prognosis
,”
Proceedings of the Seventh IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes (SAFEPROCESS 09)
.
3.
Salmasi
,
F.
, 2007, “
Control Strategies for Hybrid Electric Vehicles: Evolution, Classification, Comparison, and Future Trends
,”
IEEE Trans. Veh. Technol.
0018-9545,
56
(
5
), pp.
2393
2404
.
4.
Brahma
,
A.
,
Guezennec
,
Y.
, and
Rizzoni
,
G.
, 2000, “
Optimal Energy Management in Series Hybrid Electric Vehicles
,”
Proceedings of the 2000 American Control Conference
, Vol.
1
, pp.
60
64
.
5.
Lin
,
C. -C.
,
Peng
,
H.
,
Grizzle
,
J. W.
, and
Kang
,
J. -M.
, 2003, “
Power Management Strategy for a Parallel Hybrid Electric Truck
,”
IEEE Trans. Control Syst. Technol.
1063-6536,
11
(
6
), pp.
839
849
.
6.
Sundström
,
O.
,
Ambühl
,
D.
, and
Guzzella
,
L.
, 2009, “
On Implementation of Dynamic Programming for Optimal Control Problems With Final State Constraints
,”
Oil Gas Sci. Technol.
,
65
(
1
), pp.
91
102
.
7.
Piccolo
,
A.
,
Ippolito
,
L.
,
Galdi
,
V.
, and
Vaccaro
,
A.
, 2001, “
Optimization of Energy Flow Management in Hybrid Electric Vehicles via Genetic Algorithms
,”
Proceedings of the 2001 IEEE/ASME International Conference on Advanced Intelligent Mechatronics
, Como, Italy, July.
8.
West
,
M.
,
Bingham
,
C.
, and
Schofield
,
N.
, 2003, “
Predictive Control for Energy Management in All/More Electric Vehicles With Multiple Energy Storage Units
,”
Proceedings of the IEEE International Electric Machines and Drives Conference (IEMDC ’03)
, Vol.
1
.
9.
Borhan
,
H.
,
Vahidi
,
A.
,
Phillips
,
A.
,
Kuang
,
M.
, and
Kolmanovsky
,
I.
, 2009, “
Predictive Energy Management of a Power-Split Hybrid Electric Vehicle
,”
Proceedings of the 2009 American Control Conference
.
10.
Sampathnarayanan
,
B.
,
Serrao
,
L.
,
Onori
,
S.
,
Rizzoni
,
G.
, and
Yurkovich
,
S.
, 2009, “
Model Predictive Control as an Energy Management Strategy for Hybrid Electric Vehicle
,”
Proceedings of the Second Annual Dynamic Systems and Control Conference (DSCC 2009)
.
11.
Kolmanovsky
,
I.
,
Siverguina
,
I.
, and
Lygoe
,
B.
, 2002, “
Optimization of Powertrain Operating Policy for Feasibility Assessment and Calibration: Stochastic Dynamic Programming Approach
,”
Proceedings of the 2002 American Control Conference
, Vol.
2
, pp.
1425
1430
.
12.
Johannesson
,
L.
,
Åsbogård
,
M.
, and
Egardt
,
B.
, 2007, “
Assessing the Potential of Predictive Control for Hybrid Vehicle Powertrains Using Stochastic Dynamic Programming
,”
IEEE Trans. Intell. Transp. Syst.
1524-9050,
8
, pp.
71
83
.
13.
Tate
,
E.
,
Grizzle
,
J.
, and
Peng
,
H.
, 2008, “
Shortest Path Stochastic Control for Hybrid Electric Vehicles
,”
Int. J. Robust Nonlinear Control
1049-8923,
18
(
14
), pp.
1409
1429
.
14.
Cipollone
,
R.
, and
Sciarretta
,
A.
, 2006, “
Analysis of the Potential Performance of a Combined Hybrid Vehicle With Optimal Supervisory Control
,”
Proceedings of the 2006 IEEE International Conference on Control Applications
, pp.
2802
2807
.
15.
Serrao
,
L.
, and
Rizzoni
,
G.
, 2008, “
Optimal Control of Power Split for a Hybrid Electric Refuse Vehicle
,”
Proceedings of the 2008 American Control Conference
.
16.
Paganelli
,
G.
,
Ercole
,
G.
,
Brahma
,
A.
,
Guezennec
,
Y.
, and
Rizzoni
,
G.
, 2001, “
General Supervisory Control Policy for the Energy Optimization of Charge-Sustaining Hybrid Electric Vehicles
,”
JSAE Rev.
0389-4304,
22
(
4
), pp.
511
518
.
17.
Sciarretta
,
A.
,
Back
,
M.
, and
Guzzella
,
L.
, 2004, “
Optimal Control of Parallel Hybrid Electric Vehicles
,”
IEEE Trans. Control Syst. Technol.
1063-6536,
12
(
3
), pp.
352
363
.
18.
Musardo
,
C.
,
Rizzoni
,
G.
,
Guezennec
,
Y.
, and
Staccia
,
B.
, 2005, “
A-ECMS: An Adaptive Algorithm for Hybrid Electric Vehicle Energy Management
,”
Eur. J. Control
0947-3580,
11
(
4–5
), pp.
509
524
.
19.
Gu
,
B.
, and
Rizzoni
,
G.
, 2006, “
An Adaptive Algorithm for Hybrid Electric Vehicle Energy Management Based on Driving Pattern Recognition
,”
Proceedings of the 2006 ASME International Mechanical Engineering Congress and Exposition
.
20.
Jalil
,
N.
,
Kheir
,
N.
, and
Salman
,
M.
, 1997, “
A Rule-Based Energy Management Strategy for a Series Hybrid Vehicle
,”
Proceedings of the 1997 American Control Conference
, Vol.
1
.
21.
Salman
,
M.
,
Schouten
,
N.
, and
Kheir
,
N.
, 2000, “
Control Strategies for Parallel Hybrid Vehicles
,”
Proceedings of the 2000 American Control Conference
, Vol.
1
, pp.
524
528
.
22.
He
,
X.
,
Parten
,
M.
, and
Maxwell
,
T.
, 2005, “
Energy Management Strategies for a Hybrid Electric Vehicle
,”
Proceedings of the 2005 IEEE Vehicle Power and Propulsion Conference
, pp.
536
540
.
23.
Hofman
,
T.
,
Steinbuch
,
M.
,
van Druten
,
R.
, and
Serrarens
,
A.
, 2008, “
Rule-Based Equivalent Fuel Consumption Minimization Strategies for Hybrid Vehicles
,”
Proceedings of the 17th IFAC World Congress
.
24.
Sendur
,
P.
,
Stein
,
J. L.
,
Peng
,
H.
, and
Louca
,
L.
, 2003, “
An Algorithm for the Selection of Physical System Model Order Based on Desired State Accuracy and Computational Efficiency
,”
Proceedings of the 2003 ASME International Mechanical Engineering Congress and Exposition
.
25.
Lewis
,
F.
, and
Syrmos
,
V.
, 1995,
Optimal Control
,
Wiley-Interscience
,
New York
.
26.
Serrao
,
L.
, 2009, “
A Comparative Analysis of Energy Management Strategies for Hybrid Electric Vehicles
,” Ph.D. thesis, The Ohio State University, Columbus, OH.
27.
Sundström
,
O.
, and
Guzzella
,
L.
, 2009, “
A Generic Dynamic Programming Matlab Function
,”
Proceedings of the 18th IEEE International Conference on Control Applications
, pp.
1625
1630
.
28.
Geering
,
H. P.
, 2007,
Optimal Control With Engineering Applications
,
Springer
,
Berlin
.
29.
Paganelli
,
G.
,
Guerra
,
T.
,
Delprat
,
S.
,
Santin
,
J.
,
Delhom
,
M.
, and
Combes
,
E.
, 2000, “
Simulation and Assessment of Power Control Strategies for a Parallel Hybrid Car
,”
Proc. Inst. Mech. Eng., Part D (J. Automob. Eng.)
0954-4070,
214
(
7
), pp.
705
717
.
30.
Serrao
,
L.
,
Onori
,
S.
, and
Rizzoni
,
G.
, 2009, “
ECMS as a Realization of Pontryagin’s Minimum Principle for HEV Control
,”
Proceedings of the 2009 American Control Conference
.
31.
Chasse
,
A.
,
Sciarretta
,
A.
, and
Chauvin
,
J.
, 2010, “
Online Optimal Control of a Parallel Hybrid With Costate Adaptation Rule
,”
Proceedings of the 6th IFAC Symposium Advances in Automotive Control (AAC 2010)
.
32.
Wu
,
B.
,
Lin
,
C.
,
Filipi
,
Z.
,
Peng
,
H.
, and
Assanis
,
D.
, 2004, “
Optimal Power Management for a Hydraulic Hybrid Delivery Truck
,”
Veh. Syst. Dyn.
0042-3114,
42
(
1
), pp.
23
40
.
You do not currently have access to this content.