Free Final Time

  • David G. Hull
Part of the Mechanical Engineering Series book series (MES)


In this chapter, the optimal control problem is extended to allow the final time to be free, and the conditions for a minimum are developed anew. Allowing the final time to be free gives rise to a natural boundary condition for determining the optimal final time. Next, the Weierstrass condition and the Legendre-Clebsch condition are presented. Then, the conjugate point condition is developed for nonsingular optimal control problems (H uu > 0). Finally, several example problems are solved.


Optimal Control Problem Final Time Optimal Path Conjugate Point Natural Boundary Condition 
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Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • David G. Hull
    • 1
  1. 1.Aerospace Engineering and Engineering MechanicsThe University of Texas at AustinAustinUSA

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