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Volumn 43, Issue 1, 2005, Pages 325-340

On a representation of the limit occupational measures set of a control system with applications to singularly perturbed control systems

Author keywords

Approximation of slow motions; Averaging method; Limit occupational measures sets; Occupational measures; Singularly perturbed control systems

Indexed keywords

APPROXIMATION THEORY; MATRIX ALGEBRA; OPTIMIZATION; PERTURBATION TECHNIQUES; PROBABILITY; SET THEORY; THEOREM PROVING; TOPOLOGY; VECTORS;

EID: 14244265806     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012903424186     Document Type: Article
Times cited : (56)

References (48)
  • 1
    • 0031268841 scopus 로고    scopus 로고
    • Asymptotic optimization of a nonlinear hybrid system governed by a Markov decision process
    • E. ALTMAN AND V. GAITSGORY, Asymptotic optimization of a nonlinear hybrid system governed by a Markov decision process, SIAM J. Control Optim., 35 (1997), pp. 2070-2085.
    • (1997) SIAM J. Control Optim. , vol.35 , pp. 2070-2085
    • Altman, E.1    Gaitsgory, V.2
  • 2
    • 0036338482 scopus 로고    scopus 로고
    • Viscosity solutions methods for singular perturbations in deterministic and stochastic control
    • O. ALVAREZ AND M. BARDI, Viscosity solutions methods for singular perturbations in deterministic and stochastic control, SIAM J. Control Optim., 40 (2001), pp. 1159-1188.
    • (2001) SIAM J. Control Optim. , vol.40 , pp. 1159-1188
    • Alvarez, O.1    Bardi, M.2
  • 3
    • 0034439787 scopus 로고    scopus 로고
    • The chattering limit of singularly perturbed optimal control problems
    • Sydney
    • Z. ARTSTEIN, The chattering limit of singularly perturbed optimal control problems, in Proceedings of CDC-2000, Control and Decision Conference, Sydney, 2000, pp. 564-569.
    • (2000) Proceedings of CDC-2000, Control and Decision Conference , pp. 564-569
    • Artstein, Z.1
  • 4
    • 0036925207 scopus 로고    scopus 로고
    • An occupational measure solution to a singularly perturbed optimal control problem
    • Z. ARTSTEIN, An occupational measure solution to a singularly perturbed optimal control problem, Control Cybernet., 31 (2002), pp. 623-642.
    • (2002) Control Cybernet. , vol.31 , pp. 623-642
    • Artstein, Z.1
  • 5
    • 0031236995 scopus 로고    scopus 로고
    • Tracking fast trajectories along a slow dynamics: A singular perturbations approach
    • Z. ARTSTEIN AND V. GAITSGORY, Tracking fast trajectories along a slow dynamics: A singular perturbations approach, SIAM J. Control Optim., 35 (1997), pp. 1487-1507.
    • (1997) SIAM J. Control Optim. , vol.35 , pp. 1487-1507
    • Artstein, Z.1    Gaitsgory, V.2
  • 6
    • 0033885874 scopus 로고    scopus 로고
    • The value function of singularly perturbed control systems
    • Z. ARTSTEIN AND V. GAITSGORY, The value function of singularly perturbed control systems, Appl. Math. Optim., 41 (2000), pp. 425-445.
    • (2000) Appl. Math. Optim. , vol.41 , pp. 425-445
    • Artstein, Z.1    Gaitsgory, V.2
  • 7
    • 0041852620 scopus 로고    scopus 로고
    • Convergence to convex compact sets in infinite dimensions
    • Z. ARTSTEIN AND V. GAITSGORY, Convergence to convex compact sets in infinite dimensions, J. Math. Anal. Appl., 284 (2003), pp. 471-180.
    • (2003) J. Math. Anal. Appl. , vol.284 , pp. 471-1180
    • Artstein, Z.1    Gaitsgory, V.2
  • 8
    • 0037249145 scopus 로고    scopus 로고
    • Singularly perturbed control systems with one-dimensional fast dynamics
    • Z. ARTSTEIN AND A. LEIZAROWITZ, Singularly perturbed control systems with one-dimensional fast dynamics, SIAM J. Control Optim., 41 (2002), pp. 641-658.
    • (2002) SIAM J. Control Optim. , vol.41 , pp. 641-658
    • Artstein, Z.1    Leizarowitz, A.2
  • 11
    • 0032204231 scopus 로고    scopus 로고
    • Singular perturbation of a finite horizon problem with state-space constraints
    • F. BAGAGIOLO AND M. BARDI, Singular perturbation of a finite horizon problem with state-space constraints, SIAM J. Control Optim., 36 (1998), pp. 2040-2060.
    • (1998) SIAM J. Control Optim. , vol.36 , pp. 2040-2060
    • Bagagiolo, F.1    Bardi, M.2
  • 14
    • 14244262735 scopus 로고    scopus 로고
    • Controllability for systems with slowly varying parameters
    • F. COLONIUS AND R. FABRI, Controllability for systems with slowly varying parameters, ESAIM Control Optim. Calc. Var., 9 (2003), pp. 207-216.
    • (2003) ESAIM Control Optim. Calc. Var. , vol.9 , pp. 207-216
    • Colonius, F.1    Fabri, R.2
  • 16
    • 0026765643 scopus 로고
    • Time-scale decomposition of the reachable set of constrained linear systems
    • A. DONTCHEV, Time-scale decomposition of the reachable set of constrained linear systems, Math. Control Signals Systems, 5 (1992), pp. 327-340.
    • (1992) Math. Control Signals Systems , vol.5 , pp. 327-340
    • Dontchev, A.1
  • 17
    • 0030150904 scopus 로고    scopus 로고
    • A Tichonov-type theorem for singularly perturbed differential inclusion
    • A. DONTCHEV, T. DONCHEV, AND I. SLAVOV, A Tichonov-type theorem for singularly perturbed differential inclusion, Nonlinear Anal., 26 (1996), pp. 1547-1554.
    • (1996) Nonlinear Anal. , vol.26 , pp. 1547-1554
    • Dontchev, A.1    Donchev, T.2    Slavov, I.3
  • 18
    • 0033141127 scopus 로고    scopus 로고
    • Averaging method for one-sided Lipschitz differential inclusions with generalized solutions
    • T. DONCHEV AND I. SLAVOV, Averaging method for one-sided Lipschitz differential inclusions with generalized solutions, SIAM J. Control Optim., 37 (1999), pp. 1600-1613.
    • (1999) SIAM J. Control Optim. , vol.37 , pp. 1600-1613
    • Donchev, T.1    Slavov, I.2
  • 19
  • 21
    • 0000067126 scopus 로고
    • Use of the averaging method in control problems
    • translated from Russian
    • V. GAITSGORY, Use of the averaging method in control problems, Differential Equations, 22 (1986), pp. 1290-1299 (translated from Russian).
    • (1986) Differential Equations , vol.22 , pp. 1290-1299
    • Gaitsgory, V.1
  • 23
    • 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
  • 24
    • 0001187161 scopus 로고    scopus 로고
    • Limit occupational measures set for a control system and averaging of singularly perturbed control systems
    • V. GAITSGORY AND A. LEIZAROWITZ, Limit occupational measures set for a control system and averaging of singularly perturbed control systems, J. Math. Anal. Appl., 233 (1999), pp. 461-475.
    • (1999) J. Math. Anal. Appl. , vol.233 , pp. 461-475
    • Gaitsgory, V.1    Leizarowitz, A.2
  • 25
    • 0038198571 scopus 로고    scopus 로고
    • Multiscale singularly perturbed control systems: Limit occupational measures sets and averaging
    • V. GAITSGORY AND M.-T. NGUYEN, Multiscale singularly perturbed control systems: Limit occupational measures sets and averaging, SIAM J. Control Optim., 41 (2002), pp. 954-974.
    • (2002) SIAM J. Control Optim. , vol.41 , pp. 954-974
    • Gaitsgory, V.1    Nguyen, M.-T.2
  • 26
    • 0031168753 scopus 로고    scopus 로고
    • Averaging of singularly perturbed systems
    • G. GRAMMEL, Averaging of singularly perturbed systems, Nonlinear Anal., 28 (1997), pp. 1851-1865.
    • (1997) Nonlinear Anal. , vol.28 , pp. 1851-1865
    • Grammel, G.1
  • 27
    • 0034238659 scopus 로고    scopus 로고
    • Periodic near optimal control
    • G. GRAMMEL, Periodic near optimal control, J. Math. Anal. Appl., 248 (2000), pp. 124-144.
    • (2000) J. Math. Anal. Appl. , vol.248 , pp. 124-144
    • Grammel, G.1
  • 28
    • 0030836307 scopus 로고    scopus 로고
    • On convergence of attainability sets for controlled two-scale stochastic linear systems
    • Y. KABANOV AND S. PERGAMENSHIKOV, On convergence of attainability sets for controlled two-scale stochastic linear systems, SIAM J. Control Optim., 35 (1997), pp. 134-159.
    • (1997) SIAM J. Control Optim. , vol.35 , pp. 134-159
    • Kabanov, Y.1    Pergamenshikov, S.2
  • 30
    • 0021501125 scopus 로고
    • Applications of singular perturbation techniques to control problems
    • P.V. KOKOTOVÍC, Applications of singular perturbation techniques to control problems, SIAM Rev., 26 (1984), pp. 501-550.
    • (1984) SIAM Rev. , vol.26 , pp. 501-550
    • Kokotovíc, P.V.1
  • 33
    • 85016575106 scopus 로고
    • Approximation of continuously differentiable functions
    • North-Holland, Amsterdam
    • J.G. LLAVONA, Approximation of Continuously Differentiable Functions, North-Holland Math. Stud. 130, North-Holland, Amsterdam, 1986.
    • (1986) North-Holland Math. Stud. , vol.130
    • Llavona, J.G.1
  • 34
    • 0036303858 scopus 로고    scopus 로고
    • Order reduction is invalid for singularly perturbed control problems with a vector fast variable
    • A. LEIZAROWITZ, Order reduction is invalid for singularly perturbed control problems with a vector fast variable, Math. Control Signals Systems, 15 (2002), pp. 101-119.
    • (2002) Math. Control Signals Systems , vol.15 , pp. 101-119
    • Leizarowitz, A.1
  • 38
    • 0000404633 scopus 로고
    • Singular perturbations and optimal control
    • Mathematical Control Theory, W.A. Copel, ed., Springer-Verlag, Berlin
    • R.E. O'MALLEY, JR., Singular perturbations and optimal control, in Mathematical Control Theory, W.A. Copel, ed., Lecture Notes in Math. 680, Springer-Verlag, Berlin, 1978, pp. 170-218.
    • (1978) Lecture Notes in Math. , vol.680 , pp. 170-218
    • O'Malley Jr., R.E.1
  • 39
    • 84972502110 scopus 로고
    • Singular perturbations in non-linear optimal control systems
    • M. QUINCAMPOIX AND H. ZHANG, Singular perturbations in non-linear optimal control systems, Differential Integral Equations, 8 (1995), pp. 931-944.
    • (1995) Differential Integral Equations , vol.8 , pp. 931-944
    • Quincampoix, M.1    Zhang, H.2
  • 43
    • 0001287190 scopus 로고
    • Time-average control of a martingale problem. Existence of a stationary solution
    • R.H. STOCKBRIDGE, Time-average control of a martingale problem. Existence of a stationary solution, Ann. Probab., 18 (1990), pp. 190-205.
    • (1990) Ann. Probab. , vol.18 , pp. 190-205
    • Stockbridge, R.H.1
  • 45
    • 0031192484 scopus 로고    scopus 로고
    • A generalization of Tichonov theorem for singularly perturbed differential inclusions
    • V. VELIOV, A generalization of Tichonov theorem for singularly perturbed differential inclusions, J. Dynam. Control Systems, 3 (1997), pp. 1-28.
    • (1997) J. Dynam. Control Systems , vol.3 , pp. 1-28
    • Veliov, V.1
  • 46
    • 0030826053 scopus 로고    scopus 로고
    • Limits of singularly perturbed control problems with statistical limits of fast motions
    • A. VIGODNER, Limits of singularly perturbed control problems with statistical limits of fast motions, SIAM J. Control Optim., 35 (1997), pp. 1-28.
    • (1997) SIAM J. Control Optim. , vol.35 , pp. 1-28
    • Vigodner, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.