메뉴 건너뛰기




Volumn 35, Issue 1, 1997, Pages 134-159

On convergence of attainability sets for controlled two-scale stochastic linear systems

Author keywords

Attainability sets; Controlled stochastic differential equations; Hausdorff metric; Mayer problem; Singular perturbations; Two scale system

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; LINEAR CONTROL SYSTEMS; OPTIMIZATION; RANDOM PROCESSES; SET THEORY; STOCHASTIC CONTROL SYSTEMS;

EID: 0030836307     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012994269685     Document Type: Article
Times cited : (8)

References (20)
  • 1
    • 0015107853 scopus 로고
    • Existence of optimal control laws
    • V. E. BENEŠ, Existence of optimal control laws, SIAM J. Control, 9 (1971), pp. 446-475.
    • (1971) SIAM J. Control , vol.9 , pp. 446-475
    • Beneš, V.E.1
  • 2
    • 0002082052 scopus 로고
    • On some singular perturbation problems arising in stochastic control
    • A. BENSOUSSAN, On some singular perturbation problems arising in stochastic control, Stochastic Anal. Appl., 2 (1984), pp. 13-53.
    • (1984) Stochastic Anal. Appl. , vol.2 , pp. 13-53
    • Bensoussan, A.1
  • 5
    • 0001036732 scopus 로고
    • Singular perturbations in stochastic control
    • Singular Perturbations and Asymptotic Analysis in Control Systems, P. Kokotovič, A. Bensoussan, and G. Blankenship, eds. Springer-Verlag, Berlin
    • A. BENSOUSSAN AND G. L. BLANKENSHIP, Singular perturbations in stochastic control, in Singular Perturbations and Asymptotic Analysis in Control Systems, Lecture Notes in Control and Inform. Sci. 90, P. Kokotovič, A. Bensoussan, and G. Blankenship, eds. Springer-Verlag, Berlin, 1987.
    • (1987) Lecture Notes in Control and Inform. Sci. , vol.90
    • Bensoussan, A.1    Blankenship, G.L.2
  • 7
    • 0003256848 scopus 로고
    • Perturbations, Approximations and Sensitivity Analysis of Optimal Control Systems
    • Springer-Verlag, Berlin
    • A. L. DONTCHEV. Perturbations, Approximations and Sensitivity Analysis of Optimal Control Systems, Lecture Notes in Control and Inform. Sci. 52, Springer-Verlag, Berlin, 1983.
    • (1983) Lecture Notes in Control and Inform. Sci. , vol.52
    • Dontchev, A.L.1
  • 8
    • 0020781601 scopus 로고
    • Singular perturbation in Mayer's optimization problem for linear systems
    • A. L. DONTCHEV AND V. M. VELIOV, Singular perturbation in Mayer's optimization problem for linear systems, SIAM J. Control Optim., 21 (1983), pp. 566-581.
    • (1983) SIAM J. Control Optim. , vol.21 , pp. 566-581
    • Dontchev, A.L.1    Veliov, V.M.2
  • 10
    • 0026925030 scopus 로고
    • Suboptimization of singularly perturbed control systems
    • V. GAITSGORY, Suboptimization of singularly perturbed control systems, SIAM J. Control Optim., 30 (1992), pp. 1228-1249.
    • (1992) SIAM J. Control Optim. , vol.30 , pp. 1228-1249
    • Gaitsgory, V.1
  • 12
    • 0012876339 scopus 로고
    • On the variation distance for the probability measures defined on a filtered space
    • YU. M. KABANOV, R. SH. LIPTSER, AND A. N. SHIRYAEV, On the variation distance for the probability measures defined on a filtered space, Probability Theory Related Fields, 71 (1986), pp. 19-35.
    • (1986) Probability Theory Related Fields , vol.71 , pp. 19-35
    • Kabanov, Yu.M.1    Liptser, R.Sh.2    Shiryaev, A.N.3
  • 13
    • 3943049578 scopus 로고
    • Optimal control of singularly perturbed linear stochastic systems
    • YU. M. KABANOV AND S. M. PERGAMENSHCHIKOV, Optimal control of singularly perturbed linear stochastic systems, Stochastics Stochastics Rep., 36 (1991), pp. 109-135.
    • (1991) Stochastics Stochastics Rep. , vol.36 , pp. 109-135
    • Kabanov, Yu.M.1    Pergamenshchikov, S.M.2
  • 14
    • 0009960277 scopus 로고
    • Asymptotic expansions for singularly perturbed stochastic differential equations
    • V. V. Sazonov and T. L. Shervashidze, eds., Coronet Books, Philadelphia, PA
    • YU. M. KABANOV, S. M. PERGAMENSHCHIKOV, AND J. M. STOYANOV, Asymptotic expansions for singularly perturbed stochastic differential equations, in New Trends in Probability and Statistics, Vol. 1., V. V. Sazonov and T. L. Shervashidze, eds., Coronet Books, Philadelphia, PA, 1991, pp. 413-435.
    • (1991) New Trends in Probability and Statistics , vol.1 , pp. 413-435
    • Kabanov, Yu.M.1    Pergamenshchikov, S.M.2    Stoyanov, J.M.3
  • 15
    • 85033165500 scopus 로고    scopus 로고
    • On control of two-scale stochastic systems with linear dynamics in the fast variables
    • to appear
    • YU. M. KABANOV AND W. RUNGGALDIER, On control of two-scale stochastic systems with linear dynamics in the fast variables, Math. Control Systems Signals, to appear.
    • Math. Control Systems Signals
    • Kabanov, Yu.M.1    Runggaldier, W.2
  • 19
    • 0000952694 scopus 로고
    • A generalization of a problem of Steinhaus
    • Hung.
    • J. KOMLOŚ, A generalization of a problem of Steinhaus, Acta Math. Sci. (Hung.), 18 (1967), pp. 217-229.
    • (1967) Acta Math. Sci. , vol.18 , pp. 217-229
    • Komloś, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.