Jacobi's condition for singular extremals: An extended notion of conjugate points
✍ Scribed by R. Berlanga; J.F. Rosenblueth
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 399 KB
- Volume
- 15
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
✦ Synopsis
Communicated by F. Clarke
Abstract--For the simple fixed endpoint problem in the calculus of variations, Jacobi's condition ("there are no conjugate points in the interior of the underlying time interval") is nec~ry for optimality if the trajectory under consideration is nonsingulax. In this paper, we extend the notion of conjugate points so that the above condition (in terms of this new notion) is necessary also for singular extremals. This is achieved by showing that, without any additional assumption on the trajectory, the nonnegativity of the second variation on the space of admiesible variations is equivalent to the nonexistence of these "extended conjugate points". ~