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.