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Sufficiency for essentially bounded controls which do not satisfy the strengthened Legendre-Clebsch condition
| Content Provider | Semantic Scholar |
|---|---|
| Author | Licea, Gerardo Sánchez |
| Copyright Year | 2018 |
| Abstract | In this paper we present two new sufficiency results appropriate for optimal control problems of Lagrange subject to nonlinear dynamics, fixed end-points and nonlinear inequality and equality constraints in the controls. The main novelties of the new sufficient theorem relie strongly in the facts that the proposed optimal controls need not satisfy assumptions of regularity such as strong normality, full rankness of certain matrices depending on the control constraints, assumptions of nonsingularity as the strengthened Legendre-Clebsch condition, or smoothness conditions imposed in the optimal controls such as continuity or piecewise continuity. The positivity of the second variation over a set of admissible variations together with an appropriate condition of Weierstrass are fundamental components in the verification technique used to prove the sufficiency theorems as well as in the verification technique used to test the new sets of sufficient conditions established in this theory. Mathematics Subject Classification: 49K15 |
| Starting Page | 1297 |
| Ending Page | 1315 |
| Page Count | 19 |
| File Format | PDF HTM / HTML |
| DOI | 10.12988/ams.2018.810137 |
| Alternate Webpage(s) | http://www.m-hikari.com/ams/ams-2018/ams-25-28-2018/p/sanchezAMS25-28-2018.pdf |
| Alternate Webpage(s) | https://doi.org/10.12988/ams.2018.810137 |
| Volume Number | 12 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
