Numerical Solutions for Known Trajectories

This chapter deals with numerical solutions for the powersplit problem for hybrid vehicles using predefined power and velocity trajectories. Two numerical solution methods are pursued: an indirect method that uses the necessary conditions for optimality obtained with Pontryagin’s Minimum Principle, and a direct method using the Dynamic Programming algorithm which is based on Bellman’s Principle of Optimality. Both methods are illustrated with an example.

[1]  H. Bock,et al.  A Multiple Shooting Algorithm for Direct Solution of Optimal Control Problems , 1984 .

[2]  van Tac Thijs Keulen,et al.  Fuel optimal control of hybrid vehicles , 2011 .

[3]  Srdjan M. Lukic,et al.  Effects of drivetrain hybridization on fuel economy and dynamic performance of parallel hybrid electric vehicles , 2004, IEEE Transactions on Vehicular Technology.

[4]  Lino Guzzella,et al.  On Implementation of Dynamic Programming for Optimal Control Problems with Final State Constraints , 2010 .

[5]  Alfio Quarteroni,et al.  Numerical Mathematics (Texts in Applied Mathematics) , 2006 .

[6]  Robert D. Russell,et al.  Numerical solution of boundary value problems for ordinary differential equations , 1995, Classics in applied mathematics.

[7]  Sebastian Sager,et al.  Numerical methods for mixed-integer optimal control problems , 2006 .

[8]  Huei Peng,et al.  Power management strategy for a parallel hybrid electric truck , 2003, IEEE Trans. Control. Syst. Technol..

[9]  Ilya V. Kolmanovsky,et al.  Ultracapacitor Assisted Powertrains: Modeling, Control, Sizing, and the Impact on Fuel Economy , 2011, IEEE Transactions on Control Systems Technology.

[10]  Giorgio Rizzoni,et al.  Unified modeling of hybrid electric vehicle drivetrains , 1999 .

[11]  Zoran Filipi,et al.  Combined optimisation of design and power management of the hydraulic hybrid propulsion system for the 6 × 6 medium truck , 2004 .

[12]  Jtba John Kessels,et al.  Energy management for automotive power nets , 2007 .

[13]  Kok Lay Teo,et al.  Optimal control problems with a continuous inequality constraint on the state and the control , 2009, Autom..

[14]  M Maarten Steinbuch,et al.  Rule-based energy management strategies for hybrid vehicles , 2007 .

[15]  Thierry-Marie Guerra,et al.  Optimal control of a parallel powertrain: from global optimization to real time control strategy , 2002, Vehicular Technology Conference. IEEE 55th Vehicular Technology Conference. VTC Spring 2002 (Cat. No.02CH37367).

[16]  Michael Back,et al.  DETERMINATION OF THE FUEL-OPTIMAL TRAJECTORY FOR A VEHICLE ALONG A KNOWN ROUTE , 2002 .

[17]  Matthias Gerdts,et al.  Hamburger Beiträge zur Angewandten Mathematik A nonsmooth Newton ’ s method for discretized optimal control problems with state and control constraints , 2007 .

[18]  Stephen P. Boyd,et al.  Finding Ultimate Limits of Performance for Hybrid Electric Vehicles , 2000 .

[19]  Olle Sundström,et al.  Torque-Assist Hybrid Electric Powertrain Sizing: From Optimal Control Towards a Sizing Law , 2010, IEEE Transactions on Control Systems Technology.

[20]  R. Bellman Dynamic programming. , 1957, Science.

[21]  Dimitri P. Bertsekas,et al.  Dynamic Programming and Optimal Control, Two Volume Set , 1995 .

[22]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[23]  Mwt Michiel Koot,et al.  Energy management for vehicular electric power systems , 2006 .