Measuring Singularity of Generalized Minimizers for Control-Affine Problems
| dc.creator | Guerra, Manuel | |
| dc.creator | Sarychev, Andrey | |
| dc.date | 2008-09-13 | |
| dc.date.accessioned | 2026-07-07T10:02:46Z | |
| dc.date.available | 2026-07-07T10:02:46Z | |
| dc.description | An open question contributed by Yu. Orlov to a recently published volume "Unsolved Problems in Mathematical Systems and Control Theory", V.D. Blondel, A. Megretski (eds), Princeton Univ. Press, 2004, concerns regularization of optimal control-affine problems. These noncoercive problems in general admit 'cheap (generalized) controls' as minimizers; it has been questioned whether and under what conditions infima of the regularized problems converge to the infimum of the original problem. Starting with a study of this question we show by simple functional-theoretic reasoning that it admits, in general, positive answer. This answer does not depend on commutativity/noncommtativity of controlled vector fields. It depends instead on presence or absence of a Lavrentiev gap. We set an alternative question of measuring "singularity" of minimizing sequences for control-affine optimal control problems by so-called degree of singularity. It is shown that, in the particular case of singular linear-quadratic problems, this degree is tightly related to the "order of singularity" of the problem. We formulate a similar question for nonlinear control-affine problem and establish partial results. Some conjectures and open questions are formulated. | |
| dc.description | 40 pages | |
| dc.identifier | https://arxiv.org/abs/0809.2363 | |
| dc.identifier | http://arxiv.org/abs/0809.2363 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169092 | |
| dc.subject | Optimization and Control | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 49J15, 49J45, 49J30, 93B29 | |
| dc.title | Measuring Singularity of Generalized Minimizers for Control-Affine Problems | |
| dc.type | text |