Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Journal of Dynamical and Control Systems
Erschienen in: Journal of Dynamical and Control Systems 1/2019

04.01.2018

Optimization of Boundary Value Problems for Certain Higher-Order Differential Inclusions

verfasst von: Elimhan N. Mahmudov

Erschienen in: Journal of Dynamical and Control Systems | Ausgabe 1/2019

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The present paper studies a new class of problems of optimal control theory with special differential inclusions described by higher-order linear differential operators (HLDOs). There arises a rather complicated problem with simultaneous determination of the HLDOs and a Mayer functional depending of high-order derivatives of searched functions. The sufficient conditions, containing both the Euler-Lagrange and Hamiltonian type inclusions and “transversality” conditions at the endpoints t = − 1, 0 and t = 1 are derived. One of the key features in the proof of sufficient conditions is the notion of locally adjoint mappings. Then, we demonstrate how these conditions can be transformed into Pontryagin’s maximum principle in some particular cases.
Vorheriger Artikel Controlled Motion of a Spherical Robot with Feedback. II
Nächster Artikel Necessary First- and Second-Order Optimality Conditions in Discrete Systems with a Delay in Control

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Literatur
1.
Agrachev AA, Sachkov YL, Vol. II. Control theory from the geometric viewpoint control theory and optimization. Berlin: Springer; 2004.MATHCrossRef
2.
Aitalioubrahim M, Sajid S. Second-order viability problems with perturbation in Hilbert spaces. J Dynam Control Syst. 2010;16(4):453–469.MathSciNetMATHCrossRef
3.
Bartuzel G, Fryszkowski A. Filippov lemma for certain differential inclusion of third order. Demonstratio Math XLI. 2008;41:337–352.MathSciNetMATH
4.
Bartuzel G, Fryszkowski A. Relaxation of the differential inclusions of the Sturm-Liouville type. Demonstratio Math. 1997;30:953–960.MathSciNetMATH
5.
Benchohra JR, Graef HJ, Ntouyas SK. Nonresonance impulsive higher order functional nonconvex-valued differential inclusions. Electron J Qual Theory Differ Equ. 2002;13:1–13.MathSciNetMATHCrossRef
6.
Cannarsa P, Marigonda A, Nguyen KT. Optimality conditions and regularity results for time optimal control problems with differential inclusions. J Math Anal Appl. 2015;427(1):202–228.MathSciNetMATHCrossRef
7.
Cernea A. On the existence of solutions for a higher order differential inclusion without convexity. Electron J of Qual Theory of Differ Equ. 2007;8:1–8.MathSciNetMATHCrossRef
8.
Clarke FH, Vol. 264. Functional analysis, calculus of variations and optimal control. Graduate texts in mathematics. Berlin: Springer; 2013.CrossRef
9.
Guerra M, Sarychev AV. Approximation of generalized minimizers and regularization of optimal control problems. Lagrangian and Hamiltonian Methods for Nonlinear Control. In: Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, Vol. 366); 2006. p. 269–279.
10.
Lupulescu V. Viability result for nonconvex second order differential inclusions. Electron J Differ Equat. 2002;76:1–12.MathSciNetMATH
11.
Mahmudov EN. Sufficient conditions for optimality for differential inclusions of parabolic type and duality. J Glob Optim. 2008;41(1):31–42.MathSciNetMATHCrossRef
12.
Mahmudov EN. Duality in the problems of optimal-control for systems described by convex differential-inclusions with delay. Prob Cont Inform Theory. 1987;16(6):411–422.MathSciNet
13.
Mahmudov EN. Approximation and optimization of higher order discrete and differential inclusions. Nonlin Diff Equat Appl NoDEA. 2014;21(1):1–26.MathSciNetMATHCrossRef
14.
Mahmudov EN. Necessary and sufficient conditions for discrete and differential inclusions of elliptic type. J Math Anal Appl. 2006;323(2):768–789.MathSciNetMATHCrossRef
15.
Mahmudov EN. Approximation and optimization of discrete and differential inclusions. Waltham: Elsevier; 2011.MATH
16.
17.
Mahmudov EN. Optimal control of Cauchy problem for first-order discrete and partial differential inclusions. J Dynam Control Syst. 2009;15(4):587–610.MathSciNetMATHCrossRef
18.
Mahmudov EN. Convex optimization of second order discrete and differential inclusions with inequality constraints. J Convex Anal. 2018;25(1):1–26.MathSciNet
19.
Mordukhovich BS. Variational analysis and generalized differentiation, I: Basic Theory; II: applications, Grundlehren Series (Fundamental Principles of Mathematical Sciences). Springer. 2006;330:331.
20.
Pontryagin LS, Boltyanskii VG, Gamkrelidze RV, Mishchenko EF. The mathematical theory of optimal processes. New York: Wiley; 1965.
21.
Xianlong F. Approximate controllability for neutral impulsive differential inclusions with nonlocal conditions. J Dynam Control Syst. 2011;17(3):359–386.MathSciNetMATHCrossRef
Metadaten
Titel
Optimization of Boundary Value Problems for Certain Higher-Order Differential Inclusions
verfasst von
Elimhan N. Mahmudov
Publikationsdatum
04.01.2018
Verlag
Springer US
Erschienen in
Journal of Dynamical and Control Systems / Ausgabe 1/2019
Print ISSN: 1079-2724
Elektronische ISSN: 1573-8698
DOI
https://doi.org/10.1007/s10883-017-9392-5

Weitere Artikel der Ausgabe 1/2019

Journal of Dynamical and Control Systems 1/2019 Zur Ausgabe

OriginalPaper

Pseudo Almost Periodic Solutions to Impulsive Non-autonomous Stochastic Differential Equations with Unbounded Delay and its Optimal Control

OriginalPaper

Global Attractor for a Class of Sixth-Order Viscous Cahn-Hilliard Equation in an Unbounded Domain

OriginalPaper

Controlled Motion of a Spherical Robot with Feedback. II

OriginalPaper

Privileged Coordinates and Nilpotent Approximation of Carnot Manifolds, I. General Results

OriginalPaper

Existence and Multiplicity of Standing Wave Solutions for a Class of Quasilinear Schrödinger Systems in

OriginalPaper

Necessary First- and Second-Order Optimality Conditions in Discrete Systems with a Delay in Control

Premium Partner

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen. 

    Zur Marktübersicht
    Bildnachweise