For a given $varepsilon$>0 and a given special type set valued map t$rightarrow$V(t), t $in$ [$t_ast$,$t^ast$], it is required to define differential inclusion such that the Hausdorff distance between the reachable sets of the differential inclusion with initial set ($t_ast$,V($t_ast$)) and V(t) would be less than $varepsilon$ for every t $in$ [$t_ast$,$t^ast$].
📌 3 Key Takeaways
🎯
Objective & Hypothesis:In this article, the inverse problem of the differential inclusion theory is considered.
📊
Key Findings & Data:In this article, the inverse problem of the differential inclusion theory is considered.
💡
Conclusion & Impact:For a given $varepsilon$>0 and a given special type set valued map t$rightarrow$V(t), t $in$ [$t_ast$,$t^ast$], it is required to define differential inclusion such that the Hausdorff distance between the reachable sets of the differential inclusion with initial set ($t_ast$,V($t_ast$)) and V(t) would be less than $varepsilon$ for every t $in$ [$t_ast$,$t^ast$].
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
In this article, the inverse problem of the differential inclusion theory is considered. For a given $varepsilon$>0 and a given special type set valued map t$rightarrow$V(t), t $in$ [$t_ast$,$t^ast$], it is required to define differential inclusion such that the Hausdorff distance between the reachable sets of the differential inclusion with initial set ($t_ast$,V($t_ast$)) and V(t) would be less than $varepsilon$ for every t $in$ [$t_ast$,$t^ast$].
🔖
Cite This Article
GUSEINOV, K. G., ÖZER, O., DÜZCE, S. A. (2003). On the construction of differential inclusion with prescribed integral funnel. Mathematical and Computational Applications, Cilt: 8 - Sayı: 1, 119–126. https://ajindex.com/articles/280365
V.I.Blagodatskikh and A.F.Filippov,. Differential Inclusions and Optimal Control, Proc. of the Steklov Inst, of Math., 169, 194-252, 1985
A.B.Kurzhanski and L.Valyi, Ellipsoidal Calculus for Estimation and Control, Birkhauser, Boston, 1996
Kh.G.Guseinov, A.A.Moiseyev and V.N.Ushakov, On the Approximation of Reachable Domains of Control Systems, J. Appl Math. Mech., 62, 169-175, 1998
Kh.G.Guseinov and V.N.Ushakov, Differential Properties of Integral Funnels and Stable Bridges, J. Appl Math. Mech., 55, 56-61, 1991
Kh.G.Guseinov and V.N.Ushakov, The Construction of Differential Inclusions with Prescribed Properties, Different. Equal, 36,488-496, 2000
T.Kh.Babalyev and V.N.Ushakov, An Inverse Problem in the Theory of Differential Inclusions, Different. Equal, 34,447-453, 1998
M.Boudaoud and T.Rzezuchowski, On Differential Inclusions with Prescribed Solutions, Cos. Pestov. Math., 114,289-293, 1989
Kh.G.Guseinov, O.Ozer and S.A.Duzce, On the Convex Continuation of the Convex Compact Multivalued Map, Abstracts XII National Mathematics Symposium. 6-10 September, Malatya, Turkey. 27-30, 1999.