Journal Article

Riemannian comparison and conjugate locus in optimal control

D. McCaffrey and S. P. Banks

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 17, issue 2, pages 123-145
Published in print June 2000 | ISSN: 0265-0754
Published online June 2000 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/17.2.123
Riemannian comparison and conjugate locus in optimal control

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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.

Journal Article.  0 words. 

Subjects: Mathematics

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