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Fixed Final Time: Tests for a Minimum

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

Abstract

Before going on to the second differential, two tests for a minimal control are derived. The Weierstrass condition is based on strong variations, which means that control changes are large but that state changes are small. The Weierstrass condition requires that the Hamiltonian be an absolute minimum with respect to the control at every point of a minimal path. The Legendre-Clebsch condition is obtained by reducing strong variations to weak variations. It requires that the Hamiltonian be a local minimum with respect to the control at every point of the minimal path.

Keywords

Optimal Path Strong Variation Minimal Path Weak Variation Navigation Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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