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- Title
Riemannian comparison and conjugate locus in optimal control.
- Authors
McCaffrey, D.; Banks, S. P.
- Abstract
There is an extensive literature on second-order conditions involving conjugate points in optimal control. Applying these conditions generally involves testing the nature of solutions to Riccati or Jacobi-type equations. However this requires the evaluation of a specific extremal. This paper considers whether it is possible to estimate a priori the geometry of the entire set of points conjugate to a given final set without having to evaluate specific extremals. It is shown that this can be done for a class of problems where the dynamics and cost function are respectively linear and quadratic in the control variable and the dynamics satisfy an integrability condition. The problem is interpreted as a geodesic problem to which Rauch's comparison theorem is applied. The locus of conjugate points is estimated for some examples.
- Publication
IMA Journal of Mathematical Control & Information, 2000, Vol 17, Issue 2, p123
- ISSN
0265-0754
- Publication type
Article
- DOI
10.1093/imamci/17.2.123