| Title:
|
Derived cones to reachable sets of a nonlinear differential inclusion (English) |
| Author:
|
Cernea, Aurelian |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
139 |
| Issue:
|
4 |
| Year:
|
2014 |
| Pages:
|
567-575 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider a nonlinear differential inclusion defined by a set-valued map with nonconvex values and we prove that the reachable set of a certain variational inclusion is a derived cone in the sense of Hestenes to the reachable set of the initial differential inclusion. In order to obtain the continuity property in the definition of a derived cone we use a continuous version of Filippov's theorem for solutions of our differential inclusion. As an application, in finite dimensional spaces, we obtain a sufficient condition for local controllability along a reference trajectory. (English) |
| Keyword:
|
derived cone |
| Keyword:
|
$m$-dissipative operator |
| Keyword:
|
local controllability |
| MSC:
|
34A60 |
| MSC:
|
93B03 |
| MSC:
|
93C15 |
| idZBL:
|
Zbl 06433681 |
| idMR:
|
MR3306847 |
| DOI:
|
10.21136/MB.2014.144134 |
| . |
| Date available:
|
2015-02-04T09:08:16Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144134 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Căpraru, I., Cernea, A.: On the existence of solutions for nonlinear differential inclusions.14 pages, DOI:102478/aicu-2014-0016 (to appear) in Anal. Univ. "Al. I. Cuza", Iaşi. MR 3300732 |
| Reference:
|
[4] Cernea, A.: Local controllability of hyperbolic differential inclusions via derived cones.Rev. Roum. Math. Pures Appl. 47 (2002), 21-31. Zbl 1055.49002, MR 1978185 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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[10] Mirică, Ş.: New proof and some generalizations of the minimum principle in optimal control.J. Optimization Theory Appl. 74 (1992), 487-508. Zbl 0795.49013, MR 1181848, 10.1007/BF00940323 |
| Reference:
|
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| . |
