Banach fixed-point theorem in semilinear controllability problems - a survey

被引：27
作者：
Klamka, J. [1 ]
Babiarz, A. [1 ]
Niezabitowski, M. [1 ]
机构：
[1] Silesian Tech Univ, Inst Automat Control, 16 Akad St, PL-44100 Gliwice, Poland
来源：
BULLETIN OF THE POLISH ACADEMY OF SCIENCES-TECHNICAL SCIENCES | 2016年 / 64卷 / 01期
关键词：
complete controllability; Banach space; Hilbert space; fixed-point; infinite-dimensional space; FUNCTIONAL-DIFFERENTIAL EQUATIONS; APPROXIMATE CONTROLLABILITY; CONSTRAINED CONTROLLABILITY; STOCHASTIC CONTROLLABILITY; INTEGRODIFFERENTIAL INCLUSIONS; NONLINEAR-SYSTEMS; OBSERVABILITY; DELAY; STABILITY;
D O I：
10.1515/bpasts-2016-0004
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
The main aim of this article is to review the existing state of art concerning the complete controllability of semilinear dynamical systems. The study focus on obtaining the sufficient conditions for the complete controllability for various systems using the Banach fixed-point theorem. We describe the results for stochastic semilinear functional integro-differential system, stochastic partial differential equations with finite delays, semilinear functional equations, a stochastic semilinear system, a impulsive stochastic integro-differential system, semilinear stochastic impulsive systems, an impulsive neutral functional evolution integro-differential system and a nonlinear stochastic neutral impulsive system. Finally, two examples are presented.
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页码：21 / 35
页数：15
相关论文
共 80 条
  • [1] [Anonymous], 2001, INT J MATH MATH SCI, DOI DOI 10.1155/S0161171202111318
  • [2] [Anonymous], 1995, INTRO INFINITE DIMEN
  • [3] Controllability of nonlinear Ito type stochastic integrodifferential systems
    Balachandran, K.
    Karthikeyan, S.
    [J]. JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2008, 345 (04): : 382 - 391
  • [4] Balachandran K, 2007, KYBERNETIKA, V43, P31
  • [5] Controllability of stochastic integrodifferential systems
    Balachandran, K.
    Karthikeyan, S.
    [J]. INTERNATIONAL JOURNAL OF CONTROL, 2007, 80 (03) : 486 - 491
  • [6] Controllability of nonlinear systems in Banach spaces: A survey
    Balachandran, K
    Dauer, JP
    [J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2002, 115 (01) : 7 - 28
  • [7] On concepts of controllability for deterministic and stochastic systems
    Bashirov, AE
    Mahmudov, NI
    [J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1999, 37 (06) : 1808 - 1821
  • [8] Trajectory controllability of nonlinear integro-differential system
    Chalishajar, D. N.
    George, R. K.
    Nandakumaran, A. K.
    Acharya, F. S.
    [J]. JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2010, 347 (07): : 1065 - 1075
  • [9] Controllability of impulsive functional differential systems with infinite delay in Banach spaces
    Chang, Yong-Kui
    [J]. CHAOS SOLITONS & FRACTALS, 2007, 33 (05) : 1601 - 1609
  • [10] Czornik A, 2005, DYNAM CONT DIS SER B, V12, P165
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