Annals of Operations Research

, Volume 37, Issue 1, pp 357–373 | Cite as

Direct and indirect methods for trajectory optimization

  • O. von Stryk
  • R. Bulirsch


This paper gives a brief list of commonly used direct and indirect efficient methods for the numerical solution of optimal control problems. To improve the low accuracy of the direct methods and to increase the convergence areas of the indirect methods we suggest a hybrid approach. For this a special direct collocation method is presented. In a hybrid approach this direct method can be used in combination with multiple shooting. Numerical examples illustrate the direct method and the hybrid approach.


Constrained optimal control nonlinear dynamic systems multiple shooting direct collocation nonlinear optimization hybrid approach estimates of adjoint variables 


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Copyright information

© J.C. Baltzer AG, Scientific Publishing Company 1992

Authors and Affiliations

  • O. von Stryk
    • 1
  • R. Bulirsch
    • 1
  1. 1.Mathematisches InstitutTechnische Universität MünchenMünchen 2Germany

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