Complementary Condensing for the Direct Multiple Shooting Method

  • Christian Kirches
  • Hans Georg Bock
  • Johannes P. Schlöder
  • Sebastian Sager
Conference paper


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.


Optimal Control Problem Model Predictive Control Path Constraint Quadratic Subproblem Shooting Node 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Christian Kirches
    • 1
  • Hans Georg Bock
    • 1
  • Johannes P. Schlöder
    • 1
  • Sebastian Sager
    • 1
  1. 1.Interdisciplinary Center for Scientific Computing (IWR)University of HeidelbergHeidelbergGermany

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