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

24.01.2018

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

verfasst von: Misir J. Mardanov, Samin T. Malik

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

In the paper, an optimal control problem with a delay in control is considered. Suggesting a new approach, Euler-type necessary optimality conditions and the linearized discrete maximum principle are established. Also, the second-order necessary optimality conditions (a) based on the second variation of the objective functional and (b) for quasi-singular controls are obtained. An example to illustrate the richness of content of the suggested approach is presented.
Vorheriger Artikel Optimization of Boundary Value Problems for Certain Higher-Order Differential Inclusions
Nächster Artikel Pseudo Almost Periodic Solutions to Impulsive Non-autonomous Stochastic Differential Equations with Unbounded Delay and its Optimal 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.
Ashchepkov LT. Optimal control with discontinuous systems. Moscow: Nauka; 1987.MATH
2.
Ahlbrandt CD. Equivalence of discrete Euler equations and discrete Hamiltonian systems. J Math Anal Appl 1993;180(1):498–517.MathSciNetCrossRef
3.
Arutyunov AV, Marinkovic B. Necessary conditions for optimality in discrete optimal control problems. Vestnik MGU Ser 2005;15:43–48.
4.
5.
Bellman R. Dynamic programming. Mineola: Dover Publications: Inc.; 2003.MATH
6.
Boltyanskii VG. Optimal control of discrete systems. New York: Wiley; 1978.
7.
Butkovskii AG. On necessary and sufficient optimality conditions for impulse control systems. Avtomatika i telemekhanika 1963;24(8):1056–64.MathSciNet
8.
Chyung DH. 1968. Discrete optimal systems with time delay. IEEE Trans. Autom Control AC-13 (1).
9.
Dolezal J, Vol. 174. Optimal control discrete-time systems. Lecture notes in control and information sciences. New York: Springer; 1988.
10.
Ferreira JAS, Vidal RVV, Vol. 84. On the connections between mathematical programming and discrete optimal control. Lecture notes in control and information sciences. New York: Springer; 1986.
11.
12.
Shak FH. The theory of optimal control by discrete processes. USSR Comput Math Math Phys 1970;10(3):68–84.CrossRef
13.
Shak FH. An optimal control in discrete systems with time lag. Autom Remote Control 1065–73. 1970.
14.
Fan L-C, Chu-Sen W. Discrete maximum principle. Moscow: Mir; 1967.
15.
Gabasov R, Kirillova FM. Singular optimal control. Nauka: Moscow; 1973.MATH
16.
Gabasov R, Kirillova FM. Necessary conditions for the type of equality in discrete systems. Dif Uravn 1973;9(3):542–6.MATH
17.
Gabasov R, Kirillova FM. Concerning theory of necessary conditions of optimality for discrete systems. Autom Remote Control 1970;30(12):1921–28.MATH
18.
Gabasov R. On the theory of optimal processes in discrete systems. USSR Comput Math Math Phys 1968;8(4):99–123.MathSciNetCrossRef
19.
Gorokhovik VV, Gorokhovik Ya S, Marinkovic B. First and second order necessary optimality conditions for a discrete-time optimal control problem with a vector-valued objective function. Positivity 2013;17:483–500.MathSciNetCrossRef
20.
Hilscher R, Zeidan V. Discrete optimal control: second order optimality conditions. J Differ Equ Appl 2002;8:875–896.MathSciNetCrossRef
21.
Guardabassi G, Rinaldi S. Optimization of discrete systems with delayed control variables. A structural approach. Avtomat i Telemekh 1968;29(7):54–59.MATH
22.
Gurman VI. 1976. Optimization of discrete systems. ISU Irkutsk State University.
23.
Halkin H. On the necessary conditions for the optimal control of nonlinear systems. J Math Anal 1964;12:1–82.MathSciNetCrossRef
24.
Holtzman JM, Halkin H. Directional convexity and the maximum principle for discrete systems. SIAM J Control 1966;4(2):213–275.CrossRef
25.
Jordan BW, Polak E. Theory of a class of discrete optimal control systems. J Electron Control 1964;17(6):697–711.MathSciNetCrossRef
26.
Mansimov KB. On optimality of singular controls in the systems with delay controlled by means of initial functions. Diff Uravn 1985;25(6):1081–84.MATH
27.
Mardanov MJ, Melikov TK, Mahmudov NI. On necessary optimality conditions in discrete control systems. Int J Control 2015;88(10):2097–2106.MathSciNetCrossRef
28.
29.
Mardanov MJ, Melikov TK. A method for studying the optimality of controls is discrete systems. Proc Inst Math Mech 2014;40:3–12.MATH
30.
Vinter RB. Optimality and sensitivity of discrete time processes. Control Cybern. 1988;7(2-3):191–211.MathSciNetMATH
31.
Marinkovic B. Optimality conditions for discrete optimal control problems. Optim Method Softw 2007;22:959–969.MathSciNetCrossRef
32.
Marinkovic B. Optimality conditions in discrete optimal control problems with state constraints. Numer Funct Anal Optim 2008;28:945–955.MathSciNetCrossRef
33.
Mordukhovich BS. Approximate maximum principle for finite difference control systems. USSR Comput Maths Math Phys 1988;28:106–114.MathSciNetCrossRef
34.
Mordukhovich BS, Trubnik R. Stability of discrete approximations and necessary optimality conditions for delay-differential inclusions. Ann Oper Res 2001;101(1):149–170.MathSciNetCrossRef
35.
Smaqin VI, Smaqin SV. Adaptive inventory control with restrictions and transport delays. Bulletin of the Tomsk State University. Manag Comput Eng Inform 2008;3(4): 20–26.
36.
Gaishun IV. 2001. Gaishun, systems with discrete time. National Academy of Sciences of Belarus, Institute of Mathematics, Minsk.
37.
Polak E. Computational methods in optimization. New York: Academic Press; 1971.
38.
Propoi AI. Elements of the theory of optimal discrete processes. Nauka: Moscow; 1973.
39.
Krasovsky NN. 1957. On a optimal regulation problem. Prikladnaya matematika I mekhanika 21(5).
40.
Pontryagin LS, Boltyanskii VG, Gamkrelidze RV, Mishchenko EF. Mathematical Theory of Optimal Processes. New York: Wiley; 1962.
41.
Rozonoer LI. Pontryagin’s maximum principle in theory of optimal systems. Avtomatika i telemekhanika 20(12). 1959.
42.
Gabasov R, Kirillova FM. To the question of extending the Pontryagin maximum principle to discrete systems. Avtomat i Telemekh 1966;11:46–51.
43.
Moiseev NN. Numerical methods in theory of optimal systems. Nauka: Moscow; 1971.
44.
Rockafellar RT. Convex Analysis. Princeton: Princeton University Press; 1970.CrossRef
45.
Kwon WH, Pimenov VG, Lozhnikov AB, Han SH, Onegova OV. Time-Delay System Toolbox (for use with MATLAB), Beta Version. Seoul National University Korea. 1998.
Metadaten
Titel
Necessary First- and Second-Order Optimality Conditions in Discrete Systems with a Delay in Control
verfasst von
Misir J. Mardanov
Samin T. Malik
Publikationsdatum
24.01.2018
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/s10883-017-9394-3

Weitere Artikel der Ausgabe 1/2019

Journal of Dynamical and Control Systems 1/2019 Zur Ausgabe

OriginalPaper

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

OriginalPaper

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

OriginalPaper

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

OriginalPaper

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

OriginalPaper

Controlled Motion of a Spherical Robot with Feedback. II

OriginalPaper

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