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Differential inclusions with state constraints

Published online by Cambridge University Press:  20 January 2009

Nikolaos S. Papageorgiou
Nikolaos S. Papageorgiou
Affiliation:
Department of MathematicsUniversity of CaliforniaDavisCalifornia 95616U.S.A.
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In “Viability Theory”, we select trajectories which are viable in the sense that they always satisfy a given constraint. Since the fundamental work of Nagumo [26], we know that in order to guarantee existence of viable trajectories, we need to satisfy certain tangential conditions. In the case of differential inclusions and using the modern terminology and notation of tangent cones, this condition takes the form F(t, x) ∩ TK#φ, where F(.,.) is the orientor field involved in the differential inclusion, K is the viability (constraint) set and TK(x) is the tangent cone to K at x. Results on the existence of viable solutions for differential inclusions can be found in Aubin–Cellina [2] and Papageorgiou [30,32].

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 32 , Issue 1 , February 1989 , pp. 81 - 98
Copyright
Copyright © Edinburgh Mathematical Society 1989

References

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