MATHEMATICA BOHEMICA, Vol. 139, No. 4, pp. 567-575, 2014

Derived cones to reachable sets of a nonlinear differential inclusion

Aurelian Cernea

Aurelian Cernea, Faculty of Mathematics and Informatics, University of Bucharest, Academiei 14, 010014 Bucharest, Romania, e-mail:

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.

Keywords: derived cone; $m$-dissipative operator; local controllability

Classification (MSC 2010): 34A60, 93C15

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