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Complementary Condensing for the Direct Multiple Shooting Method

In: Modeling, Simulation and Optimization of Complex Processes

Author

Listed:
  • Christian Kirches

    (University of Heidelberg, Interdisciplinary Center for Scientific Computing (IWR))

  • Hans Georg Bock

    (University of Heidelberg, Interdisciplinary Center for Scientific Computing (IWR))

  • Johannes P. Schlöder

    (University of Heidelberg, Interdisciplinary Center for Scientific Computing (IWR))

  • Sebastian Sager

    (University of Heidelberg, Interdisciplinary Center for Scientific Computing (IWR))

Abstract

In this contribution we address the efficient solution of optimal control problems of dynamic processes with many controls. Such problems typically arise from the convexification of integer control decisions. We treat this problem class using the direct multiple shooting method to discretize the optimal control problem. The resulting nonlinear problems are solved using an SQP method. Concerning the solution of the quadratic subproblems we present a factorization of the QP’s KKT system, based on a combined null-space range-space approach exploiting the problem’s block sparse structure. We demonstrate the merit of this approach for a vehicle control problem in which the integer gear decision is convexified.

Suggested Citation

  • Christian Kirches & Hans Georg Bock & Johannes P. Schlöder & Sebastian Sager, 2012. "Complementary Condensing for the Direct Multiple Shooting Method," Springer Books, in: Hans Georg Bock & Xuan Phu Hoang & Rolf Rannacher & Johannes P. Schlöder (ed.), Modeling, Simulation and Optimization of Complex Processes, edition 127, pages 195-206, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-25707-0_16
    DOI: 10.1007/978-3-642-25707-0_16
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