Geodesic
Derived cones to reachable sets of a nonlinear differential inclusion
Mathematica Bohemica, Tome 139 (2014) no. 4, pp. 567-575

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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.
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.
DOI : 10.21136/MB.2014.144134
Classification : 34A60, 93B03, 93C15
Keywords: derived cone; $m$-dissipative operator; local controllability 
Cernea, Aurelian. Derived cones to reachable sets of a nonlinear differential inclusion. Mathematica Bohemica, Tome 139 (2014) no. 4, pp. 567-575. doi: 10.21136/MB.2014.144134
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