Handling State Constraints in Fast-computing Optimal Control for Hybrid Powertrains

Abstract To optimally design hybrid powertrains, optimal energy management strategies must be automatically and rapidly generated. Pontryagin’s minimum principle-derived optimization tool called Hybrid Optimization Tool (HOT) can guarantee the fast computing of minimal fuel consumption using an array operation as well as Picard’s method. However, in presence of state constraints (e.g., the battery state of charge limitations), the near-optimality of HOT no longer holds. Herein, we use the interior- and exterior-penalty method to impose the state constraints in HOT and highlight numerical difficulties encountered in their implementation. Then, a factor that causes the numerical difficulties is optimized by quantifying trade-off between the state constraints violation and computational demanding. Finally, through a case study of a parallel hybrid electric vehicle, the results show that despite of a complex problem with rapidly changing dynamics, the penalty methods are able to generate results comparable with dynamic programming ones while guaranteeing the low computational burden.

[1]  Alexandre Chasse,et al.  Supervisory control of hybrid powertrains: An experimental benchmark of offline optimization and online energy management , 2009 .

[2]  A. Q. Xing,et al.  Applications of the exterior penalty method in constrained optimal control problems , 1989 .

[3]  Anders Grauers,et al.  Optimal Sizing of a Parallel PHEV Powertrain , 2013, 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]  A. Q. Xing,et al.  The Exact Penalty Function Method in Constrained Optimal Control Problems , 1994 .

[6]  Suresh P. Sethi,et al.  A Survey of the Maximum Principles for Optimal Control Problems with State Constraints , 1995, SIAM Rev..

[7]  Cristian H. De Angelo,et al.  Determination of the Equivalent Consumption in Hybrid Electric Vehicles in the State-Constrained Case , 2016 .

[8]  Lino Guzzella,et al.  Vehicle Propulsion Systems , 2013 .

[9]  Lorenzo Serrao,et al.  Open Issues in Supervisory Control of Hybrid Electric Vehicles: A Unified Approach Using Optimal Control Methods , 2013 .

[10]  Simona Onori,et al.  A Comparative Analysis of Energy Management Strategies for Hybrid Electric Vehicles , 2011 .

[11]  Peter Falb,et al.  Some successive approximation methods in control and oscillation theory , 1972 .

[12]  Antonio Sciarretta,et al.  Design and Control Co-Optimization for Hybrid Powertrains: Development of Dedicated Optimal Energy Management Strategy , 2016 .

[13]  N. Petit,et al.  An interior penalty method for optimal control problems with state and input constraints of nonlinear systems , 2016 .

[14]  Gérard Bloch,et al.  Optimizing fuel consumption and pollutant emissions of gasoline-HEV with catalytic converter , 2017 .

[15]  L. Guzzella,et al.  Control of hybrid electric vehicles , 2007, IEEE Control Systems.

[16]  Anil V. Rao,et al.  Trajectory Optimization: A Survey , 2014 .

[17]  Daeheung Lee,et al.  A jump condition of PMP-based control for PHEVs , 2011 .

[18]  Maarten Steinbuch,et al.  Solution for state constrained optimal control problems applied to power split control for hybrid vehicles , 2014, Autom..