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Research Papers

Approximate Stochastic Differential Dynamic Programming for Hybrid Vehicle Energy Management

[+] Author and Article Information
Kyle Williams

School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47906
e-mail: kwilliams@alumni.purdue.edu

Monika Ivantysynova

Maha Fluid Power Research Center,
School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47906
e-mail: mivantys@purdue.edu

1Present address: Caterpillar Large Power Systems Division, Lafayette, IN 47905.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received June 2, 2018; final manuscript received December 11, 2018; published online January 14, 2019. Assoc. Editor: Mahdi Shahbakhti.

J. Dyn. Sys., Meas., Control 141(5), 051003 (Jan 14, 2019) (9 pages) Paper No: DS-18-1264; doi: 10.1115/1.4042253 History: Received June 02, 2018; Revised December 11, 2018

This paper develops a new computational approach for energy management in a hydraulic hybrid vehicle. The developed algorithm, called approximate stochastic differential dynamic programming (ASDDP) is a variant of the classic differential dynamic programming algorithm. The simulation results are discussed for two Environmental Protection Agency drive cycles and one real world cycle based on collected data. Flexibility of the ASDDP algorithm is demonstrated as real-time driver behavior learning, and forecasted road grade information are incorporated into the control setup. Real-time potential of ASDDP is evaluated in a hardware-in-the-loop (HIL) experimental setup.

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References

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Figures

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Fig. 2

Propagation of Pr[wn=wj|w0=wi] for wi=(2.23 m/s2)

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Fig. 3

Propagation of driver acceleration demand along horizon. Expected path shown in solid dark curve, sample average shown in solid light curve, individual sample paths shown in thin light curves, standard deviations shown in dashed dark curves. Top row: UDDS cycle, middle row: US06 cycle, bottom row: Global Positioning System (GPS) cycle. Left column: w0=−1 m/s2, middle column: w0=0.6 m/s2, right column: w0=1.3 m/s2.

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Fig. 6

UDDS cycle cross training metrics. Star markers: ASDDP using stats from GPS (solid), US06 (dashed). Square markers: APDDP using stats from GPS (solid), US06 (dashed). Thick dashed: DDP. Thick solid: InstOpt.

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Fig. 7

US06 cycle cross training metrics. Star markers: ASDDP using stats from UDDS (solid), GPS (dashed). Square markers: APDDP using stats from UDDS (solid), GPS (dashed). Thick dashed: DDP. Thick solid: InstOpt.

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Fig. 8

GPS cycle cross training metrics. Star markers: ASDDP using stats from UDDS (solid), US06 (dashed). Square markers: APDDP using stats from UDDS (solid), US06 (dashed). Thick dashed: DDP. Thick solid: InstOpt.

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Fig. 9

Hardware-in-the-loop experiment results compared to simulation, GPS cycle

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