Abstract
In this chapter, the second differential is investigated to obtain the LegendreClebsch condition and the Jacobi or conjugate point condition. First, the second differential is obtained by taking the differential of the first differential. Second, the Legendre-Clebsch condition is derived from the second differential. Third, for the class of nonsingular problems (H uu > 0) conditions are developed for the existence of a neighboring optimal path. Finally, these conditions are used to develop a sufficient condition for the existence of a weak relative minimum.
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© 2003 Springer Science+Business Media New York
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Hull, D.G. (2003). Fixed Final Time: Second Differential. In: Optimal Control Theory for Applications. Mechanical Engineering Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4180-3_11
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DOI: https://doi.org/10.1007/978-1-4757-4180-3_11
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2299-1
Online ISBN: 978-1-4757-4180-3
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