-
1
-
-
0036338482
-
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 (2002), 1159-1188
-
(2002)
SIAM J. Control Optim
, vol.40
, pp. 1159-1188
-
-
Alvarez, O.1
Bardi, M.2
-
2
-
-
85130890032
-
Multiscale singular perturbations and homogenization of optimal control problems
-
O. Alvarez, M. Bardi and C. Marchi, Multiscale singular perturbations and homogenization of optimal control problems, in Geometric Control and Nonsmooth Analysis, vol. 76, World Scientific, Singapore, (2008), 1-27
-
(2008)
Geometric Control and Nonsmooth Analysis, vol. 76, World Scientific, Singapore
, pp. 1-27
-
-
Alvarez, O.1
Bardi, M.2
Marchi, C.3
-
3
-
-
36049037276
-
Multiscale problems and homogenization for secondorder hamilton-jacobi equations
-
O. Alvarez, M. Bardi and C. Marchi, Multiscale problems and homogenization for secondorder hamilton-jacobi equations, J. Differential Equations, 243 (2007), 349-387
-
(2007)
J. Differential Equations
, vol.243
, pp. 349-387
-
-
Alvarez, O.1
Bardi, M.2
Marchi, C.3
-
5
-
-
9644282182
-
On singularly perturbed ordinary differential equations with measure-valued limits
-
Z. Artstein, On singularly perturbed ordinary differential equations with measure-valued limits, Math. Bohem., 127 (2002), 139-152
-
(2002)
Math. Bohem
, vol.127
, pp. 139-152
-
-
Artstein, Z.1
-
6
-
-
79960636922
-
Optimal control of open quantum systems applied to the photochemistry of surfaces
-
E. Asplund and T. Klüner, Optimal control of open quantum systems applied to the photochemistry of surfaces, Phys. Rev. Lett., 106 (2011), 140404
-
(2011)
Phys. Rev. Lett
, vol.106
-
-
Asplund, E.1
Klüner, T.2
-
7
-
-
0001036732
-
Singular perturbations in stochastic control
-
(eds. P. V. Kokotovic, A. Bensoussan and G. L. Blankenship), vol. 90 of Lecture Notes in Control and Information Sciences, Springer Berlin Heidelberg
-
A. Bensoussan and G. Blankenship, Singular perturbations in stochastic control, in Singular Perturbations and Asymptotic Analysis in Control Systems (eds. P. V. Kokotovic, A. Bensoussan and G. L. Blankenship), vol. 90 of Lecture Notes in Control and Information Sciences, Springer Berlin Heidelberg, (1987), 171-260
-
(1987)
Singular Perturbations and Asymptotic Analysis in Control Systems
, pp. 171-260
-
-
Bensoussan, A.1
Blankenship, G.2
-
9
-
-
84972565055
-
An ergodic control problem arising from the principal eigenvalue of an elliptic operator
-
A. Bensoussan and H. Nagai, An ergodic control problem arising from the principal eigenvalue of an elliptic operator, J. Math. Soc. Japan, 43 (1991), 49-65
-
(1991)
J. Math. Soc. Japan
, vol.43
, pp. 49-65
-
-
Bensoussan, A.1
Nagai, H.2
-
10
-
-
34250245856
-
Martingales, the malliavin calculus and hypoellipticity under general hörmander's conditions
-
J.-M. Bismut, Martingales, the malliavin calculus and hypoellipticity under general hörmander's conditions, Z. Wahrsch. Verw. Gebiete, 56 (1981), 469-505
-
(1981)
Z. Wahrsch. Verw. Gebiete
, vol.56
, pp. 469-505
-
-
Bismut, J.-M.1
-
11
-
-
0032061556
-
Probabilistic approach to homogenizations of systems of quasilinear parabolic PDEs with periodic structures
-
R. Buckdahn and Y. Hu, Probabilistic approach to homogenizations of systems of quasilinear parabolic PDEs with periodic structures, Nonlinear Analysis, 32 (1998), 609-619
-
(1998)
Nonlinear Analysis
, vol.32
, pp. 609-619
-
-
Buckdahn, R.1
Hu, Y.2
-
12
-
-
0041128049
-
Probabilistic approach to homogenization of viscosity solutions of parabolic pdes
-
R. Buckdahn, Y. Hu and S. Peng, Probabilistic approach to homogenization of viscosity solutions of parabolic pdes, NoDEA Nonlinear Differential Equations Appl., 6 (1999), 395-411
-
(1999)
NoDEA Nonlinear Differential Equations Appl
, vol.6
, pp. 395-411
-
-
Buckdahn, R.1
Hu, Y.2
Peng, S.3
-
13
-
-
33646471733
-
Benchmark examples for model reduction of linear time invariant dynamical systems, Dimension Reduction of Large-Scale Systems
-
Y. Chahlaoui and P. Van Dooren, Benchmark examples for model reduction of linear time invariant dynamical systems, in Dimension Reduction of Large-Scale Systems, vol. 45 of Lect. Notes Comput. Sci. Eng., (2005), 379-392
-
(2005)
vol. 45 of Lect. Notes Comput. Sci. Eng
, pp. 379-392
-
-
Chahlaoui, Y.1
Van Dooren, P.2
-
14
-
-
0030374474
-
Connections between stochastic control and dynamic games
-
P. Dai Pra, L. Meneghini and W. Runggaldier, Connections between stochastic control and dynamic games, Mathematics of Control, Signals and Systems, 9 (1996), 303-326
-
(1996)
Mathematics of Control, Signals and Systems
, vol.9
, pp. 303-326
-
-
Dai Pra, P.1
Meneghini, L.2
Runggaldier, W.3
-
15
-
-
0000637746
-
Portfolio selection with transaction costs
-
M. H. Davis and A. R. Norman, Portfolio selection with transaction costs, Math. Oper. Res., 15 (1990), 676-713
-
(1990)
Math. Oper. Res
, vol.15
, pp. 676-713
-
-
Davis, M.H.1
Norman, A.R.2
-
16
-
-
84861503544
-
Importance sampling for multiscale diffusions
-
P. Dupuis, K. Spiliopoulos and H. Wang, Importance sampling for multiscale diffusions, Mul-tiscale Model. Simul., 10 (2012), 1-27
-
(2012)
Mul-tiscale Model. Simul
, vol.10
, pp. 1-27
-
-
Dupuis, P.1
Spiliopoulos, K.2
Wang, H.3
-
17
-
-
22244431981
-
Importance sampling. large deviations. and differential games
-
P. Dupuis and H. Wang, Importance sampling, large deviations, and differential games, Stochastics and Stochastic Reports, 76 (2004), 481-508
-
(2004)
Stochastics and Stochastic Reports
, vol.76
, pp. 481-508
-
-
Dupuis, P.1
Wang, H.2
-
18
-
-
84971110219
-
The perturbed test function method for viscosity solutions of nonlinear PDE
-
L. C. Evans, The perturbed test function method for viscosity solutions of nonlinear PDE, P. Roy. Soc. Edinb. A, 111 (1989), 359-375
-
(1989)
P. Roy. Soc. Edinb. A
, vol.111
, pp. 359-375
-
-
Evans, L.C.1
-
19
-
-
0001234347
-
Risk-sensitive control on an infinite time horizon
-
W. H. Fleming and W. M. McEneaney, Risk-sensitive control on an infinite time horizon, SIAM J. Control Optim., 33 (1995), 1881-1915
-
(1995)
SIAM J. Control Optim
, vol.33
, pp. 1881-1915
-
-
Fleming, W.H.1
McEneaney, W.M.2
-
21
-
-
0026925030
-
Suboptimization of singularly perturbed control systems
-
V. Gaitsgory, Suboptimization of singularly perturbed control systems, SIAM J .Control Optim., 30 (1992), 1228-1249
-
(1992)
SIAM J .Control Optim
, vol.30
, pp. 1228-1249
-
-
Gaitsgory, V.1
-
23
-
-
0021441691
-
All optimal Hankel-norm approximations of linear multivariable systems and their L1-error bounds
-
K. Glover, All optimal Hankel-norm approximations of linear multivariable systems and their L1-error bounds, Int. J. Control, 39 (1984), 1115-1193
-
(1984)
Int. J. Control
, vol.39
, pp. 1115-1193
-
-
Glover, K.1
-
24
-
-
0031168753
-
Averaging of singularly perturbed systems
-
G. Grammel, Averaging of singularly perturbed systems, Nonlinear Analysis, 28 (1997), 1851-1865
-
(1997)
Nonlinear Analysis
, vol.28
, pp. 1851-1865
-
-
Grammel, G.1
-
25
-
-
4544354870
-
A survey of model reduction by balanced truncation and some new results
-
S. Gugercin and A. Antoulas, A survey of model reduction by balanced truncation and some new results, Int. J. Control, 77 (2004), 748-766
-
(2004)
Int. J. Control
, vol.77
, pp. 748-766
-
-
Gugercin, S.1
Antoulas, A.2
-
26
-
-
80052883821
-
Balanced model reduction of partially observed Langevin equations: An averaging principle
-
C. Hartmann, Balanced model reduction of partially observed Langevin equations: An averaging principle, Math. Comput. Model. Dyn. Syst., 17 (2011), 463-490
-
(2011)
Math. Comput. Model. Dyn. Syst
, vol.17
, pp. 463-490
-
-
Hartmann, C.1
-
27
-
-
84884835715
-
Balanced averaging of bilinear systems with applications to stochastic control
-
C. Hartmann, B. Schäfer-Bung and A. Zueva, Balanced averaging of bilinear systems with applications to stochastic control, J. Control Optim., 51 (2013), 2356-2378
-
(2013)
J. Control Optim
, vol.51
, pp. 2356-2378
-
-
Hartmann, C.1
Schäfer-Bung, B.2
Zueva, A.3
-
28
-
-
84868569168
-
Efficient rare event simulation by optimal nonequilibrium forcing
-
C. Hartmann and C. Schütte, Efficient rare event simulation by optimal nonequilibrium forcing, J. Stat. Mech. Theor. Exp., 2012 (2012), P11004
-
(2012)
J. Stat. Mech. Theor. Exp
, vol.2012
-
-
Hartmann, C.1
Schütte, C.2
-
29
-
-
77956763488
-
Balanced truncation of linear second-order systems: A Hamiltonian approach
-
C. Hartmann, V. Vulcanov and C. Schütte, Balanced truncation of linear second-order systems: A Hamiltonian approach, Multiscale Model. Simul., 8 (2010), 1348-1367
-
(2010)
Multiscale Model. Simul
, vol.8
, pp. 1348-1367
-
-
Hartmann, C.1
Vulcanov, V.2
Schütte, C.3
-
30
-
-
84980156723
-
A minimum principle for the principal eigenvalue for second-order linear elliptic equations with natural boundary conditions
-
C. J. Holland, A minimum principle for the principal eigenvalue for second-order linear elliptic equations with natural boundary conditions, Comm. Pure Appl. Math., 31 (1978), 509-519
-
(1978)
Comm. Pure Appl. Math
, vol.31
, pp. 509-519
-
-
Holland, C.J.1
-
31
-
-
63549106706
-
A stochastic representation for fully nonlinear PDEs and its application to homogenization
-
N. Ichihara, A stochastic representation for fully nonlinear PDEs and its application to homogenization, J. Math. Sci. Univ. Tokyo, 12 (2005), 467-492
-
(2005)
J. Math. Sci. Univ. Tokyo
, vol.12
, pp. 467-492
-
-
Ichihara, N.1
-
32
-
-
84888334025
-
Dimensional reduction in nonlinear filtering: A homogenization approach
-
P. Imkeller, N. S. Namachchivaya, N. Perkowski and H. C. Yeong, Dimensional reduction in nonlinear filtering: A homogenization approach, Ann. Appl. Probab., 23 (2013), 2290-2326
-
(2013)
Ann. Appl. Probab
, vol.23
, pp. 2290-2326
-
-
Imkeller, P.1
Namachchivaya, N.S.2
Perkowski, N.3
Yeong, H.C.4
-
33
-
-
14244262317
-
-
Springer, Berlin, Heidelberg, Paris
-
Y. Kabanov and S. Pergamenshchikov, Two-scale Stochastic Systems: Asymptotic Analysis and Control, Springer, Berlin, Heidelberg, Paris, 2003
-
(2003)
Two-scale Stochastic Systems: Asymptotic Analysis and Control
-
-
Kabanov, Y.1
Pergamenshchikov, S.2
-
34
-
-
0021501125
-
Applications of singular perturbation techniques to control problems
-
P. V. Kokotovic, Applications of singular perturbation techniques to control problems, SIAM Review, 26 (1984), 501-550
-
(1984)
SIAM Review
, vol.26
, pp. 501-550
-
-
Kokotovic, P.V.1
-
35
-
-
0043268633
-
Singular perturbation techniques in control theory
-
(eds. P. V. Kokotovic, A. Bensoussan and G. L. Blankenship), vol. 90 of Lecture Notes in Control and Information Sciences, Springer Berlin Heidelberg
-
P. Kokotovic, Singular perturbation techniques in control theory, in Singular Perturbations and Asymptotic Analysis in Control Systems (eds. P. V. Kokotovic, A. Bensoussan and G. L. Blankenship), vol. 90 of Lecture Notes in Control and Information Sciences, Springer Berlin Heidelberg, (1987), 1-55
-
(1987)
Singular Perturbations and Asymptotic Analysis in Control Systems
, pp. 1-55
-
-
Kokotovic, P.1
-
36
-
-
1942498781
-
Stationary solutions and forward equations for controlled and singular martingale problems
-
T. Kurtz and R. H. Stockbridge, Stationary solutions and forward equations for controlled and singular martingale problems, Electron. J. Probab, 6 (2001), 52pp
-
(2001)
Electron. J. Probab
, vol.6
, pp. 52
-
-
Kurtz, T.1
Stockbridge, R.H.2
-
37
-
-
85035026377
-
Direct averaging and perturbed test function methods for weak convergence
-
H. J. Kushner, Direct averaging and perturbed test function methods for weak convergence, Lect. Notes Contr. Inf., 81 (1986), 412-426
-
(1986)
Lect. Notes Contr. Inf
, vol.81
, pp. 412-426
-
-
Kushner, H.J.1
-
40
-
-
79961242531
-
A structure-preserving numerical discretization of reversible diffusions
-
J. C. Latorre, P. Metzner, C. Hartmann and C. Schütte, A structure-preserving numerical discretization of reversible diffusions, Commun. Math. Sci., 9 (2011), 1051-1072
-
(2011)
Commun. Math. Sci
, vol.9
, pp. 1051-1072
-
-
Latorre, J.C.1
Metzner, P.2
Hartmann, C.3
Schütte, C.4
-
42
-
-
0041357028
-
Correctors for the homogenization of hamilton-jacobi equations in the stationary ergodic setting
-
P.-L. Lions and P. E. Souganidis, Correctors for the homogenization of hamilton-jacobi equations in the stationary ergodic setting, Commun. Pure Appl. Math., 56 (2003), 1501-1524
-
(2003)
Commun. Pure Appl. Math
, vol.56
, pp. 1501-1524
-
-
Lions, P.-L.1
Souganidis, P.E.2
-
43
-
-
0002684408
-
Stochastic calculus of variations and hypoelliptic operators
-
P. Malliavin, Stochastic calculus of variations and hypoelliptic operators, in Proceedings of the International Conference on Stochastic Differential Equations 1976, Wiley, New York, (1978), 195-263
-
(1978)
Proceedings of the International Conference on Stochastic Differential Equations 1976, Wiley, New York
, pp. 195-263
-
-
Malliavin, P.1
-
44
-
-
0019533482
-
Principal component analysis in linear system: Controllability. observability and model reduction
-
B. Moore, Principal component analysis in linear system: Controllability, observability and model reduction, IEEE Trans. Automat. Control, 26 (1981), 17-32
-
(1981)
IEEE Trans. Automat. Control
, vol.26
, pp. 17-32
-
-
Moore, B.1
-
46
-
-
0000315621
-
A general convergence result for a functional related to the theory of homogenization
-
G. Nguetseng, A general convergence result for a functional related to the theory of homogenization, SIAM J. Math. Anal., 20 (1989), 608-623
-
(1989)
SIAM J. Math. Anal
, vol.20
, pp. 608-623
-
-
Nguetseng, G.1
-
48
-
-
0003529370
-
-
Elsevier, Burlington, MA
-
G. Papanicolaou, A. Bensoussan and J. Lions, Asymptotic Analysis for Periodic Structures, Elsevier, Burlington, MA, 1978
-
(1978)
Asymptotic Analysis for Periodic Structures
-
-
Papanicolaou, G.1
Bensoussan, A.2
Lions, J.3
-
49
-
-
69849095791
-
Maximum likelihood drift estimation for multiscale diffusions
-
A. Papavasiliou, G. A. Pavliotis and A. M. Stuart, Maximum likelihood drift estimation for multiscale diffusions, Stochastic Process. Appl., 119 (2009), 3173-3210
-
(2009)
Stochastic Process. Appl
, vol.119
, pp. 3173-3210
-
-
Papavasiliou, A.1
Pavliotis, G.A.2
Stuart, A.M.3
-
50
-
-
74849090136
-
Dimensional reduction in nonlinear filtering
-
J. H. Park, R. B. Sowers and N. S. Namachchivaya, Dimensional reduction in nonlinear filtering, Nonlinearity, 23 (2010), 305-324
-
(2010)
Nonlinearity
, vol.23
, pp. 305-324
-
-
Park, J.H.1
Sowers, R.B.2
Namachchivaya, N.S.3
-
51
-
-
34247359516
-
Parameter estimation for multiscale diffusions
-
G. A. Pavliotis and A. M. Stuart, Parameter estimation for multiscale diffusions, J. Stat. Phys., 127 (2007), 741-781
-
(2007)
J. Stat. Phys
, vol.127
, pp. 741-781
-
-
Pavliotis, G.A.1
Stuart, A.M.2
-
53
-
-
77955419579
-
-
Stochastic modelling and applied probability, Springer, Berlin, Heidelberg
-
H. Pham, Continuous-time Stochastic Control and Optimization with Financial Applications, Stochastic modelling and applied probability, Springer, Berlin, Heidelberg, 2009
-
(2009)
Continuous-time Stochastic Control and Optimization with Financial Applications
-
-
Pham, H.1
-
54
-
-
0042361167
-
Long-term average cost control problems for continuous time Markov processes: A survey
-
M. Robin, Long-term average cost control problems for continuous time Markov processes: A survey, Acta Appl. Math., 1 (1983), 281-299
-
(1983)
Acta Appl. Math
, vol.1
, pp. 281-299
-
-
Robin, M.1
-
55
-
-
84865692627
-
Optimal control of molecular dynamics using markov state models
-
C. Schütte, S. Winkelmann and C. Hartmann, Optimal control of molecular dynamics using markov state models, Math. Program. Ser. B, 134 (2012), 259-282
-
(2012)
Math. Program. Ser. B
, vol.134
, pp. 259-282
-
-
Schütte, C.1
Winkelmann, S.2
Hartmann, C.3
-
56
-
-
38349172645
-
Laser aligned molecules: Applications in physics and chemistry
-
H. Stapelfeldt, Laser aligned molecules: Applications in physics and chemistry, Physica Scripta, 2004 (2004), 132-136
-
(2004)
Physica Scripta
, vol.2004
, pp. 132-136
-
-
Stapelfeldt, H.1
-
57
-
-
84919623957
-
Optimal control of robot guided laser material treatment
-
(eds. A. D. Fitt, J. Norbury, H. Ockendon and E. Wilson), Springer Berlin Heidelberg, (2010)
-
A. Steinbrecher, Optimal control of robot guided laser material treatment, in Progress in In-dustrial Mathematics at ECMI 2008 (eds. A. D. Fitt, J. Norbury, H. Ockendon and E. Wilson), Springer Berlin Heidelberg, (2010), 505-511
-
(2008)
Progress in In-dustrial Mathematics at ECMI
, pp. 505-511
-
-
Steinbrecher, A.1
-
58
-
-
0030826053
-
Limits of singularly perturbed control problems with statistical dynamics of fast motions
-
A. Vigodner, Limits of singularly perturbed control problems with statistical dynamics of fast motions, SIAM J. Control Optim., 35 (1997), 1-28
-
(1997)
SIAM J. Control Optim
, vol.35
, pp. 1-28
-
-
Vigodner, A.1
-
59
-
-
24044525604
-
On singular perturbations for differential inclusions on the infinite interval
-
F. Watbled, On singular perturbations for differential inclusions on the infinite interval, J. Math. Anal. Appl., 310 (2005), 362-378
-
(2005)
J. Math. Anal. Appl
, vol.310
, pp. 362-378
-
-
Watbled, F.1
-
60
-
-
0022111472
-
Exit problem and control theory
-
J. Zabczyk, Exit problem and control theory, Syst. Control Lett., 6 (1985), 165-172
-
(1985)
Syst. Control Lett
, vol.6
, pp. 165-172
-
-
Zabczyk, J.1
|