-
1
-
-
1442336159
-
Riemannian geometry of Grassmann manifolds with a view on algorithmic computation
-
P. A. ABSIL, R. MAHONY, AND R. SEPULCHRE, Riemannian geometry of Grassmann manifolds with a view on algorithmic computation, Acta Appl. Math., 80 (2004), pp. 199-220.
-
(2004)
Acta Appl. Math
, vol.80
, pp. 199-220
-
-
ABSIL, P.A.1
MAHONY, R.2
SEPULCHRE, R.3
-
2
-
-
84884085211
-
-
Princeton University Press, Princeton, NJ
-
P. A. ABSIL, R. MAHONY, AND R. SEPULCHRE, Optimization Algorithms on Matrix Manifolds, Princeton University Press, Princeton, NJ, 2007.
-
(2007)
Optimization Algorithms on Matrix Manifolds
-
-
ABSIL, P.A.1
MAHONY, R.2
SEPULCHRE, R.3
-
3
-
-
84874532872
-
Extremal problems of coding theory, in Coding Theory and Cryptography
-
H. Niederreiter, ed, World Scientific, Singapore
-
A. BARG, Extremal problems of coding theory, in Coding Theory and Cryptography, H. Niederreiter, ed., Notes of Lectures at the Institute for Mathematical Sciences of the University of Singapore, World Scientific, Singapore, 2002, pp. 1-48.
-
(2002)
Notes of Lectures at the Institute for Mathematical Sciences of the University of Singapore
, pp. 1-48
-
-
BARG, A.1
-
4
-
-
0036713221
-
Bounds on packings of spheres in the Grassmann manifold
-
A. BARG AND D.Y. NOGIN, Bounds on packings of spheres in the Grassmann manifold, IEEE Trans. Inform. Theory, 48 (2002), pp. 2450-2454.
-
(2002)
IEEE Trans. Inform. Theory
, vol.48
, pp. 2450-2454
-
-
BARG, A.1
NOGIN, D.Y.2
-
5
-
-
33847200755
-
Leader/follower synchronization of satellite attitude without angular velocity measurements
-
IEEE Press, Piscataway, NJ
-
A. K. BONDHUS, K. Y. PETTERSEN, AND J. T. GRAVDAHL, Leader/follower synchronization of satellite attitude without angular velocity measurements, in Proceedings of the 44th IEEE Conference on Decision and Control, IEEE Press, Piscataway, NJ, 2005, pp. 7270-7277.
-
(2005)
Proceedings of the 44th IEEE Conference on Decision and Control
, pp. 7270-7277
-
-
BONDHUS, A.K.1
PETTERSEN, K.Y.2
GRAVDAHL, J.T.3
-
6
-
-
0002412868
-
Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems
-
R. W. BROCKETT, Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems, Linear Algebra Appl., 146 (1991), pp. 79-91.
-
(1991)
Linear Algebra Appl
, vol.146
, pp. 79-91
-
-
BROCKETT, R.W.1
-
7
-
-
33746076163
-
-
Imperial College London, London, UK, Available online at
-
M. BROOKES, Matrix Reference Manual, Imperial College London, London, UK, 2005. Available online at http://www.ee.ie.ac.uk/hp/staff/ dmb/matrix/intro.html.
-
(2005)
Matrix Reference Manual
-
-
BROOKES, M.1
-
8
-
-
60349131623
-
-
F. BULLO AND R. MURRAY (ADVISOR), Nonlinear Control of Mechanical Systems: A Riemannian Geometry Approach, Ph.D. thesis, CalTech, Pasadena, CA, 1998.
-
F. BULLO AND R. MURRAY (ADVISOR), Nonlinear Control of Mechanical Systems: A Riemannian Geometry Approach, Ph.D. thesis, CalTech, Pasadena, CA, 1998.
-
-
-
-
9
-
-
0003232417
-
Spherical averages and applications to spherical splines and interpolation
-
S. R. BUSS AND J. P. FILLMORE, Spherical averages and applications to spherical splines and interpolation, ACM Trans. Graphics, 20 (2001), pp. 95-126.
-
(2001)
ACM Trans. Graphics
, vol.20
, pp. 95-126
-
-
BUSS, S.R.1
FILLMORE, J.P.2
-
10
-
-
0003365565
-
Spectral Graph Theory
-
AMS, Providence, RI
-
F. R. K. CHUNG, Spectral Graph Theory, Reg. Conf. Ser. Math. 92, AMS, Providence, RI, 1997.
-
(1997)
Reg. Conf. Ser. Math
, pp. 92
-
-
CHUNG, F.R.K.1
-
11
-
-
0030519411
-
-
J. H. CONWAY, R. H. HARDIN, AND N. J. A. SLOANE, Packing lines, planes, etc.: Packings in Grassmannian spaces, Exper. Math., 5 (1996), pp. 139-159.
-
J. H. CONWAY, R. H. HARDIN, AND N. J. A. SLOANE, Packing lines, planes, etc.: Packings in Grassmannian spaces, Exper. Math., 5 (1996), pp. 139-159.
-
-
-
-
12
-
-
14344256543
-
Coordinated deployment of mobile sensing networks with limited-range interactions
-
IEEE Press, Piscataway, NJ
-
J. CORTES, S. MARTINEZ, AND F. BULLO, Coordinated deployment of mobile sensing networks with limited-range interactions, in Proceedings of the 43rd IEEE Conference on Decision and Control, IEEE Press, Piscataway, NJ, 2004, pp. 1944-1949.
-
(2004)
Proceedings of the 43rd IEEE Conference on Decision and Control
, pp. 1944-1949
-
-
CORTES, J.1
MARTINEZ, S.2
BULLO, F.3
-
13
-
-
0000351907
-
Orientation statistics
-
T. D. DOWNS, Orientation statistics, Biometrika, 59 (1972), pp. 665-676.
-
(1972)
Biometrika
, vol.59
, pp. 665-676
-
-
DOWNS, T.D.1
-
14
-
-
0032216898
-
The geometry of algorithms with orthogonality constraints
-
A. EDELMAN, T. A. ARIAS, AND S. T. SMITH, The geometry of algorithms with orthogonality constraints, SIAM J. Matrix Anal. Appl., 20 (1998), pp. 303-353.
-
(1998)
SIAM J. Matrix Anal. Appl
, vol.20
, pp. 303-353
-
-
EDELMAN, A.1
ARIAS, T.A.2
SMITH, S.T.3
-
15
-
-
21144463704
-
A concept of the mass center of a system of material points in the constant curvature spaces
-
G. A. GALPERIN, A concept of the mass center of a system of material points in the constant curvature spaces, Comm. Math. Phys., 154 (1993), pp. 63-84.
-
(1993)
Comm. Math. Phys
, vol.154
, pp. 63-84
-
-
GALPERIN, G.A.1
-
16
-
-
3242726574
-
Newton's method, zeroes of vector fields, and the Riemannian center of mass
-
D. GROISSER, Newton's method, zeroes of vector fields, and the Riemannian center of mass, Adv. Appl. Math., 33 (2004), pp. 95-135.
-
(2004)
Adv. Appl. Math
, vol.33
, pp. 95-135
-
-
GROISSER, D.1
-
19
-
-
0020118274
-
Neural networks and physical systems with emergent collective computational capabilities
-
J. J. HOPFIELD, Neural networks and physical systems with emergent collective computational capabilities, Proc. Nat. Acad. Sci., 79 (1982), pp. 2554-2558.
-
(1982)
Proc. Nat. Acad. Sci
, vol.79
, pp. 2554-2558
-
-
HOPFIELD, J.J.1
-
21
-
-
33646990011
-
Chain recurrence, semiflows, and gradients
-
M. HURLEY, Chain recurrence, semiflows, and gradients, J. Dynam. Differential Equations, 7 (1995), pp. 437-456.
-
(1995)
J. Dynam. Differential Equations
, vol.7
, pp. 437-456
-
-
HURLEY, M.1
-
22
-
-
0038548185
-
Coordination of groups of mobile autonomous agents using nearest neighbor rules
-
A. JADBABAIE, J. LIN, AND A. S. MORSE, Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Trans. Automat. Control, 48 (2003), pp. 988-1001.
-
(2003)
IEEE Trans. Automat. Control
, vol.48
, pp. 988-1001
-
-
JADBABAIE, A.1
LIN, J.2
MORSE, A.S.3
-
23
-
-
1542313301
-
A Simple Control Law for UAV Formation Flying
-
Tech. report TR 2002-38, ISR, University of Maryland, College Park, MD
-
E. JUSTH AND P. KRISHNAPRASAD, A Simple Control Law for UAV Formation Flying, Tech. report TR 2002-38, ISR, University of Maryland, College Park, MD, 2002.
-
(2002)
-
-
JUSTH, E.1
KRISHNAPRASAD, P.2
-
24
-
-
84980162923
-
Riemannian center of mass and mollifier smoothing
-
H. KARCHER, Riemannian center of mass and mollifier smoothing, Comm. Pure Appl. Math., 30 (1977), pp. 509-541.
-
(1977)
Comm. Pure Appl. Math
, vol.30
, pp. 509-541
-
-
KARCHER, H.1
-
25
-
-
33947535101
-
Coordinated attitude control of satellites in formation
-
Group Coordination and Cooperative Control, Springer-Verlag, Berlin
-
T. R. KROGSTAD AND J. T. GRAVDAHL, Coordinated attitude control of satellites in formation, in Group Coordination and Cooperative Control, Lecture Notes in Control and Inform. Sci. 336, Springer-Verlag, Berlin, 2006, pp. 153-170.
-
(2006)
Lecture Notes in Control and Inform. Sci
, vol.336
, pp. 153-170
-
-
KROGSTAD, T.R.1
GRAVDAHL, J.T.2
-
26
-
-
0000856704
-
Self-entertainment of population of coupled nonlinear oscillators
-
Proceedings of the International Symposium on Mathematical Problems in Theoretical Physics, Springer-Verlag, Berlin
-
Y. KURAMOTO, Self-entertainment of population of coupled nonlinear oscillators, in Proceedings of the International Symposium on Mathematical Problems in Theoretical Physics, Lecture Notes in Phys. 39, Springer-Verlag, Berlin, 1975, pp. 420-422.
-
(1975)
Lecture Notes in Phys
, vol.39
, pp. 420-422
-
-
KURAMOTO, Y.1
-
27
-
-
0036681137
-
Synchronized multiple spacecraft rotations
-
J. R. LAWTON AND R. W. BEARD, Synchronized multiple spacecraft rotations, Automatica, 38 (2002), pp. 1359-1364.
-
(2002)
Automatica
, vol.38
, pp. 1359-1364
-
-
LAWTON, J.R.1
BEARD, R.W.2
-
28
-
-
33947394634
-
Collective motion, sensor networks and ocean sampling
-
N. E. LEONARD, D. PALEY, F. LEKIEN, R. SEPULCHRE, D. FRANTANTONI, AND R. DAVIS, Collective motion, sensor networks and ocean sampling, Proc. IEEE, 95 (2007), pp. 48-74.
-
(2007)
Proc. IEEE
, vol.95
, pp. 48-74
-
-
LEONARD, N.E.1
PALEY, D.2
LEKIEN, F.3
SEPULCHRE, R.4
FRANTANTONI, D.5
DAVIS, R.6
-
29
-
-
1442319254
-
Grassmannian manifolds as subsets of Euclidean spaces
-
A. MACHADO AND I. SALAVESSA, Grassmannian manifolds as subsets of Euclidean spaces, Res. Notes in Math., 131 (1985), pp. 85-102.
-
(1985)
Res. Notes in Math
, vol.131
, pp. 85-102
-
-
MACHADO, A.1
SALAVESSA, I.2
-
30
-
-
0000703838
-
Asymptotically autonomous semi-flows, chain recurrence and Lyapunov functions
-
K. MISCHAIKOW, H. SMITH, AND H. R. THIEME, Asymptotically autonomous semi-flows, chain recurrence and Lyapunov functions, Trans. AMS, 347 (1995), pp. 1669-1685.
-
(1995)
Trans. AMS
, vol.347
, pp. 1669-1685
-
-
MISCHAIKOW, K.1
SMITH, H.2
THIEME, H.R.3
-
31
-
-
0037281553
-
Means and averaging in the group of rotations
-
M. MOAKHER, Means and averaging in the group of rotations:, SIAM J. Matrix Anal. Appl., 24 (2002), pp. 1-16.
-
(2002)
SIAM J. Matrix Anal. Appl
, vol.24
, pp. 1-16
-
-
MOAKHER, M.1
-
32
-
-
14244267540
-
Stability of continuous-time distributed consensus algorithms
-
IEEE Press, Piscataway, NJ
-
L. MOREAU, Stability of continuous-time distributed consensus algorithms, in Proceedings of the 43rd IEEE Conference on Decision and Control, IEEE Press, Piscataway, NJ, 2004, pp. 3998-4003.
-
(2004)
Proceedings of the 43rd IEEE Conference on Decision and Control
, pp. 3998-4003
-
-
MOREAU, L.1
-
33
-
-
12944293796
-
Stability of multi-agent systems with time-dependent communication links
-
L. MOREAU, Stability of multi-agent systems with time-dependent communication links, IEEE Trans. Automat. Control, 50 (2005), pp. 169-182.
-
(2005)
IEEE Trans. Automat. Control
, vol.50
, pp. 169-182
-
-
MOREAU, L.1
-
34
-
-
14544303268
-
Stabilization of a coordinated network of rotating rigid bodies
-
IEEE Press, Piscataway, NJ
-
S. NAIR AND N. E. LEONARD, Stabilization of a coordinated network of rotating rigid bodies, in Proceedings of the 43rd IEEE Conference on Decision and Control, IEEE Press, Piscataway, NJ, 2004, pp. 4690-4695.
-
(2004)
Proceedings of the 43rd IEEE Conference on Decision and Control
, pp. 4690-4695
-
-
NAIR, S.1
LEONARD, N.E.2
-
35
-
-
4644244041
-
Consensus problems in networks of agents with switching topology and time-delays
-
R. OLFATI-SABER AND R. M. MURRAY, Consensus problems in networks of agents with switching topology and time-delays, IEEE Trans. Automat. Control, 49 (2004), pp. 1520-1533.
-
(2004)
IEEE Trans. Automat. Control
, vol.49
, pp. 1520-1533
-
-
OLFATI-SABER, R.1
MURRAY, R.M.2
-
36
-
-
29344445901
-
Probabilities and Statistics on Riemannian Manifolds: A Geometric Approach
-
5093, INRIA, Le Chesnay, France
-
X. PENNEC, Probabilities and Statistics on Riemannian Manifolds: A Geometric Approach, Research report 5093, INRIA, Le Chesnay, France, 2004.
-
(2004)
Research report
-
-
PENNEC, X.1
-
37
-
-
33947284798
-
Discrete-time synchronization on the N-torus
-
Kyoto, Japan
-
A. SARLETTE, R. SEPULCHRE, AND N. E. LEONARD, Discrete-time synchronization on the N-torus, in Proceedings of the 17th Annual International Symposium on Mathematical Theory of Networks and Systems, Kyoto, Japan, 2006, pp. 2408-2414.
-
(2006)
Proceedings of the 17th Annual International Symposium on Mathematical Theory of Networks and Systems
, pp. 2408-2414
-
-
SARLETTE, A.1
SEPULCHRE, R.2
LEONARD, N.E.3
-
38
-
-
79960981186
-
-
A. SARLETTE, R. SEPULCHRE, AND N. E. LEONARD, Cooperative attitude synchronization in satellite swarms: A consensus approach, in Proceedings of the 17th IFAC Symposium on Automatic Control in Aerospace, Toulouse, France, D. Alazard, ed., CD-Rom, 2007.
-
A. SARLETTE, R. SEPULCHRE, AND N. E. LEONARD, Cooperative attitude synchronization in satellite swarms: A consensus approach, in Proceedings of the 17th IFAC Symposium on Automatic Control in Aerospace, Toulouse, France, D. Alazard, ed., CD-Rom, 2007.
-
-
-
-
39
-
-
33947263146
-
Synchronization and balancing on the N-torus
-
L. SCARDOVI, A. SARLETTE, AND R. SEPULCHRE, Synchronization and balancing on the N-torus, Systems Control Lett., 56 (2007), pp. 335-341.
-
(2007)
Systems Control Lett
, vol.56
, pp. 335-341
-
-
SCARDOVI, L.1
SARLETTE, A.2
SEPULCHRE, R.3
-
40
-
-
39649118363
-
Collective optimization over average quantities
-
IEEE Press, Piscataway, NJ
-
L. SCARDOVI AND R. SEPULCHRE, Collective optimization over average quantities, in Proceedings of the 45th IEEE Conference on Decision and Control, IEEE Press, Piscataway, NJ, 2006, pp. 3369-3374.
-
(2006)
Proceedings of the 45th IEEE Conference on Decision and Control
, pp. 3369-3374
-
-
SCARDOVI, L.1
SEPULCHRE, R.2
-
41
-
-
33947507473
-
Group coordination and cooperative control of steered particles in the plane
-
Group Coordination and Cooperative Control, Springer-Berlin, Verlag
-
R. SEPULCHRE, D. PALEY, AND N. E. LEONARD, Group coordination and cooperative control of steered particles in the plane, in Group Coordination and Cooperative Control, Lecture Notes in Control and Inform. Sci. 336, Springer-Berlin, Verlag, 2006, pp. 217-232.
-
(2006)
Lecture Notes in Control and Inform. Sci
, vol.336
, pp. 217-232
-
-
SEPULCHRE, R.1
PALEY, D.2
LEONARD, N.E.3
-
42
-
-
34249023580
-
Stabilization of planar collective motion with all-to-all communication
-
R. SEPULCHRE, D. PALEY, AND N. E. LEONARD, Stabilization of planar collective motion with all-to-all communication, IEEE Trans. Automat. Control, 52 (2007), pp. 811-824.
-
(2007)
IEEE Trans. Automat. Control
, vol.52
, pp. 811-824
-
-
SEPULCHRE, R.1
PALEY, D.2
LEONARD, N.E.3
-
43
-
-
42649110982
-
Stabilization of planar collective motion with limited communication
-
R. SEPULCHRE, D. PALEY, AND N. E. LEONARD, Stabilization of planar collective motion with limited communication, IEEE Trans. Automat. Control, 53 (2008), pp. 706-719.
-
(2008)
IEEE Trans. Automat. Control
, vol.53
, pp. 706-719
-
-
SEPULCHRE, R.1
PALEY, D.2
LEONARD, N.E.3
-
44
-
-
0039592729
-
From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled nonlinear oscillators
-
S. H. STROGATZ, From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled nonlinear oscillators, Phys. D, 143 (2000), pp. 1-20.
-
(2000)
Phys. D
, vol.143
, pp. 1-20
-
-
STROGATZ, S.H.1
-
46
-
-
0022703065
-
Distributed asynchronous optimal routing in data networks
-
J. N. TSITSIKLIS AND D. P. BERTSEKAS, Distributed asynchronous optimal routing in data networks, IEEE Trans. Automat. Control, 31 (1986), pp. 325-332.
-
(1986)
IEEE Trans. Automat. Control
, vol.31
, pp. 325-332
-
-
TSITSIKLIS, J.N.1
BERTSEKAS, D.P.2
-
47
-
-
0022783899
-
Distributed asynchronous deterministic and stochastic gradient optimization algorithms
-
J. N. TSITSIKLIS, D. P. BERTSEKAS, AND M. ATHANS, Distributed asynchronous deterministic and stochastic gradient optimization algorithms, IEEE Trans. Automat. Control, 31 (1986), pp. 803-812.
-
(1986)
IEEE Trans. Automat. Control
, vol.31
, pp. 803-812
-
-
TSITSIKLIS, J.N.1
BERTSEKAS, D.P.2
ATHANS, M.3
-
48
-
-
0001730998
-
Novel type of phase transition in a system of self-driven particles
-
T. VICSEK, A. CZIRÓK, E. BEN- JACOB, I. COHEN, AND O. SHOCHET, Novel type of phase transition in a system of self-driven particles, Phys. Rev. Lett., 75 (1995), pp. 1226-1229.
-
(1995)
Phys. Rev. Lett
, vol.75
, pp. 1226-1229
-
-
VICSEK, T.1
CZIRÓK, A.2
BEN- JACOB, E.3
COHEN, I.4
SHOCHET, O.5
-
49
-
-
0016995661
-
Lyapunov functions for diagonally dominant systems
-
J. C. WILLEMS, Lyapunov functions for diagonally dominant systems, Automatica, 12 (1976), pp. 519-523.
-
(1976)
Automatica
, vol.12
, pp. 519-523
-
-
WILLEMS, J.C.1
|