Top

Hint

Swipe to navigate through the articles of this issue

Published in:

30-01-2019

Non-stationary Differential-Difference Games of Neutral Type

Authors: Ievgen Liubarshchuk, Yaroslav Bihun, Igor Cherevko

Published in: Dynamic Games and Applications | Issue 3/2019

Abstract

We consider the pursuit problem for 2-person conflict-controlled process with single pursuer and single evader. The problem is given by the system of the linear functional-differential equations of neutral type. The players pursue their own goals and choose controls in the form of functions of a certain kind. The goal of the pursuer is to catch the evader in the shortest possible time. The goal of the evader is to avoid the meeting of the players’ trajectories on a whole semiinfinite interval of time or if it is impossible to maximally postpone the moment of meeting. For such a conflict-controlled process, we derive conditions on its parameters and initial state, which are sufficient for the trajectories of the players to meet at a certain moment of time for any counteractions of the evader.

previous article On Time-Optimal Problems with Lifeline

next article Differential Games on Minmax of the Positional Quality Index

To get access to this content you need the following product:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

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

über 69.000 Bücher
über 500 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 90 Tage mit der neuen Mini-Lizenz testen!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 50.000 Bücher
über 380 Zeitschriften

aus folgenden Fachgebieten:

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

Jetzt 90 Tage mit der neuen Mini-Lizenz testen!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 58.000 Bücher
über 300 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt 90 Tage mit der neuen Mini-Lizenz testen!

inform now

Altmann E, Pourtallier O (2001) Advances in dynamic games and applications. Birkhäuser, Boston. https://doi.org/10.1007/978-1-4612-0155-7 CrossRef

Aubin J, Frankowska H (1990) Set-valued analysis. Birkhäuser, Boston MATH

Aumann R (1965) Integrals of set valued functions. J. Math. Anal. Appl. 12:1–12 MathSciNetCrossRefMATH

Bellman R, Cooke K (1963) Differential-difference equations. Academic Press, New York MATH

Chikrii A (1995) Multivalued mappings and their selections in game control problems. J Autom Inf Sci 27(1):27–38 MathSciNet

Chikrii A (1996) Quasilinear controlled processes under conflict. J Math Sci 80(1):1489–1518 MathSciNetCrossRefMATH

Chikrii A (2008) Optimization of game interaction of fractional-order controlled systems. Optim Methods Softw 23(1):39–72 MathSciNetCrossRefMATH

Chikrii A (2008) Game dynamic problems for systems with fractional derivatives. In: Chinchuluun A, Pardalos PM, Migdalas A, Pitsoulis L (eds) Pareto optimality, game theory and equilibria. Springer optimization and its applications, vol 17. Springer, Berlin, pp 349–387

Chikrii A (2010) An analytical method in dynamic pursuit games. Proc Steklov Inst Math 271:69–85 MathSciNetCrossRefMATH

10.

Chikrii A (2013) Conflict-controlled processes. Springer, Berlin

11.

Eidel’man S, Chikrii A (2001) Game problems of control for quasilinear systems with fractional Riemann–Liouville derivatives. Kibern Sist Anal 6:66–99

12.

Hajek O (1975) Pursuit games. Mathematics in science and engineering. Academic, New York

13.

Halanay A (1966) Differential equations: stability, oscillations, time lags. Academic Press, New York MATH

14.

Hale J (1977) Theory of functional differential equations. Springer, New York CrossRefMATH

15.

Isaacs R (1965) Differential games: a mathematical theory with applications to warfare and pursuit, control and optimization. Wiley, New York MATH

16.

Krasovskii N (1968) Theory of Motion control, linear systems. Nauka, Moscow (in Russian)

17.

Kumkov S, Le Ménec S, Patsko V (2017) Zero-sum pursuit-evasion differential games with many objects: survey of publications. Dynamic games and applications 7:609. https://doi.org/10.1007/s13235-016-0209-z MathSciNetCrossRefMATH

18.

Nikolskii M (1982) Stroboscopic strategies and the first direct Pontryagin’s method in quasilinear nonstationary differential pursuit-evasion games. Problems of control and information theory/Problemy Upravlen. Teor Inform 11(5):373–377 MathSciNet

19.

Pilipenko Y, Chikrii A (1993) Oscilatory conflict-control processes. Prikl Mat Mech 57(3):3–14 MathSciNet

20.

Pittsyk M, Chikrii A (1982) On a group pursuit problem. J Appl Math Mech 46(5):584–589 MathSciNetCrossRefMATH

21.

Pontryagin L (1966) On the theory of differential games. Russ Math Surv 21:4 MathSciNetCrossRef

22.

Pontryagin L, Boltyanskii V, Gamkrelidze R, Mischenko E (1962) The mathematical theory of optimal processes. Wiley (Interscience), New York

23.

Pshenichnyi B, Chikrii A (1977) The differential game of evasion. Izv AN SSSR Tekh Kibern 1:3–10 (in Russian)

Title: Non-stationary Differential-Difference Games of Neutral Type
Authors: Ievgen Liubarshchuk
Yaroslav Bihun
Igor Cherevko
Publication date: 30-01-2019
Publisher: Springer US
Published in: Dynamic Games and Applications / Issue 3/2019
Print ISSN: 2153-0785
Electronic ISSN: 2153-0793
DOI: https://doi.org/10.1007/s13235-019-00298-z

Springer Professional

Hint

Swipe to navigate through the articles of this issue

Abstract

Please log in to get access to this content

To get access to this content you need the following product:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Other articles of this Issue 3/2019

Continuous-Time Markov Games with Asymmetric Information

On a Solution of a Guarantee Optimization Problem Under the Functional Constraints on the Disturbance

Computation of Solvability Set for Differential Games in the Plane with Simple Motion and Non-convex Terminal Set

Krasovskii–Subbotin Approach to Mean Field Type Differential Games

Generation of Dangerous Disturbances for Flight Systems

Preface: DGAA Special Issue on Pursuit-Evasion Games and Differential Games with Incomplete Information

Premium Partner