Abstract
Thus far we have derived four sets of necessary conditions which must be met by a function x*(·) that furnishes a minimum of the integral J(·) over the class of admissible functions X; they are the conditions of Euler, Weierstrass, Legendre, and Jacobi. Now we consider conditions that must be met at a corner of x*(·), that is, at a point [t c , x*(t c )], t c ∈(t 0, t 1), where ẋ*(·) is discontinuous. These conditions are often referred to as the Erdmann-Weierstrass corner conditions.† The first of them is embodied in the following theorem.
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© 1981 Springer Science+Business Media New York
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Leitmann, G. (1981). Corner Conditions. In: The Calculus of Variations and Optimal Control. Mathematical Concepts and Methods in Science and Engineering, vol 24. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0333-4_7
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DOI: https://doi.org/10.1007/978-1-4899-0333-4_7
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-0335-8
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