Fast solution of periodic optimal control problems in automobile test-driving with gear shifts

Optimal control problems involving time-dependent decisions from a finite set have gained much interest lately, as they occur in practical applications with a high potential for optimization. A typical application is automobile driving with gear shifts. Recent work [7], [8], [9] lead to a tremendous speedup in computational times to obtain optimal solutions, allowing for more complex scenarios. In this paper we extend a benchmark mixed-integer optimal control problem to a more complicated case in which a periodic solution on a closed track is considered. Our generic solution approach is based on a convexification and relaxation of the integer control constraint. It may also be used for other objectives, such as energy minimization. Using the direct multiple shooting method we solve the new benchmark problem and present numerical results.

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

[2]  M. Gerdts.  Solving mixed‐integer optimal control problems by branch&bound: a case study from automobile test‐driving with gear shift , 2005 .

[3]  Gerhard Reinelt,et al.  Direct methods with maximal lower bound for mixed-integer optimal control problems , 2009, Math. Program..

[4]  H. Bock.  Numerical Treatment of Inverse Problems in Chemical Reaction Kinetics , 1981 .

[5]  Hans B. Pacejka,et al.  THE MAGIC FORMULA TYRE MODEL , 1991 .

[6]  H. Bock,et al.  Time‐optimal control of automobile test drives with gear shifts , 2010 .

[7]  Matthias Gerdts,et al.  A variable time transformation method for mixed‐integer optimal control problems , 2006 .

[8]  Johannes P. Schlöder,et al.  An efficient multiple shooting based reduced SQP strategy for large-scale dynamic process optimization: Part II: Software aspects and applications , 2003, Comput. Chem. Eng..

[9]  Sebastian Engell,et al.  Determining SMB Superstructures by Mixed-Integer Optimal Control , 2006, OR.

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

[11]  Olaf Stursberg,et al.  Applied Hybrid System Optimization: An Empirical Investigation of Complexity ? , 2004 .

[12]  Wolfgang Dahmen,et al.  Introduction to Model Based Optimization of Chemical Processes on Moving Horizons , 2001 .

[13]  Johannes P. Schlöder,et al.  An efficient multiple shooting based reduced SQP strategy for large-scale dynamic process optimization. Part 1: theoretical aspects , 2003, Comput. Chem. Eng..