Derived cones to reachable sets of a nonlinear differential inclusion

Aurelian Cernea

Mathematica Bohemica (2014)

  • Volume: 139, Issue: 4, page 567-575
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Cernea, Aurelian. "Derived cones to reachable sets of a nonlinear differential inclusion." Mathematica Bohemica 139.4 (2014): 567-575. <http://eudml.org/doc/269856>.

@article{Cernea2014,
abstract = {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.},
author = {Cernea, Aurelian},
journal = {Mathematica Bohemica},
keywords = {derived cone; $m$-dissipative operator; local controllability; derived cone; -dissipative operator; local controllability},
language = {eng},
number = {4},
pages = {567-575},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Derived cones to reachable sets of a nonlinear differential inclusion},
url = {http://eudml.org/doc/269856},
volume = {139},
year = {2014},
}

TY - JOUR
AU - Cernea, Aurelian
TI - Derived cones to reachable sets of a nonlinear differential inclusion
JO - Mathematica Bohemica
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 139
IS - 4
SP - 567
EP - 575
AB - 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.
LA - eng
KW - derived cone; $m$-dissipative operator; local controllability; derived cone; -dissipative operator; local controllability
UR - http://eudml.org/doc/269856
ER -

References

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  9. Lakshmikantham, V., Leela, S., Nonlinear Differential Equations in Abstract Spaces, International Series in Nonlinear Mathematics: Theory, Methods and Applications 2 Pergamon Press, Oxford (1981). (1981) Zbl0456.34002MR0616449
  10. Mirică, Ş., 10.1007/BF00940323, J. Optimization Theory Appl. 74 (1992), 487-508. (1992) Zbl0795.49013MR1181848DOI10.1007/BF00940323
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