caa a22 4500 477037143 CHVBK 20180405111308.0 cr unu---uuuuu 170330e19960301xx s 000 0 eng 10.1007/BF02434050 doi (NATIONALLICENCE)springer-10.1007/BF02434050 Shekhar S. Oak Ridge National Laboratory, 37831, Oak Ridge, TN, USA aut Local characterization of invariant sets of an autonomous differential inclusion [Elektronische Daten] Boundary of unstable manifolds [S. Shekhar] Summary: An application in robotics motivates us to characterize the evolution of a subset in state space due to a compact neighborhood of an arbitrary dynamical system—an instance of a differential inclusion. Earlier results of Blagodat·skikh and Filippov (1986) and Butkovskii (1982) characterize the boundary of theattainable set and theforward projection operator of a state. Our first result is a local characterization of the boundary of the forward projection ofa compact regular subset of the state space. Let the collection of states such that the differential inclusion contains an equilibrium point be called asingular invariant set. We show that the fields at the boundary of the forward projection of a singular invariant set are degenerate under some regularity assumptions when the state-wise boundary of the differential inclusion is smooth. Consider instead those differential inclusions such that the state-wise boundary of the problem is a regular convex polytope—a piecewise smooth boundary rather than smooth. Our second result gives conditions for theuniqueness andexistence of the boundary of the forward projection of a singular invariant set. They characterize the bundle of unstable and stable manifolds of such a differential inclusion. Springer-Verlag New York Inc, 1996 Differential inclusions nationallicence unstable and stable manifolds nationallicence stability boundaries nationallicence multivalued differential equations nationallicence control uncertainty nationallicence fine-motion planning nationallicence robotics nationallicence Journal of Nonlinear Science Springer-Verlag 6/2(1996-03-01), 105-138 0938-8974 6:2<105 1996 6 332 https://doi.org/10.1007/BF02434050 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02434050 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Shekhar S. Oak Ridge National Laboratory, 37831, Oak Ridge, TN, USA aut NATIONALLICENCE 773 0- Journal of Nonlinear Science Springer-Verlag 6/2(1996-03-01), 105-138 0938-8974 6:2<105 1996 6 332 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer