Fetching the paper…
Reading the bibliography…
We consider the problem of minimum energy steering of a linear stochastic system to a final prescribed distribution over a finite horizon and to maintain a stationary distribution over an infinite horizon.
E. Schrödinger, “Über die Umkehrung der Naturgesetze,” Sitzungsberichte der Preuss Akad. Wissen. Phys. Math. Klasse, Sonderausgabe , vol. IX, pp. 144–153, 1931
1931
Earlier work this paper cites.
——, “Sur la théorie relativiste de l’électron et l’interprétation de la mécanique quantique,” in Annales de l’institut Henri Poincaré , vol. 2, no. 4. Presses Universitaires de France, 1932, pp. 269–310
1932
Earlier work this paper cites.
R. Fortet, “Résolution d’un système d’équations de M. Schrödinger,” Math. Pures. Appl. , vol. IX, p. 83Ð105, 1940
1940
Earlier work this paper cites.
A. Beurling, “An automorphism of product measures,” The Annals of Mathematics , vol. 72, no. 1, pp. 189–200, 1960
1960
Earlier work this paper cites.
J. C. Willems, “Least squares stationary optimal control and the algebraic riccati equation,” Automatic Control, IEEE Transactions on , vol. 16, no. 6, pp. 621–634, 1971
1971
Earlier work this paper cites.
B. Jamison, “Reciprocal processes,” Z. Wahrscheinlichkeitstheorie verw. Gebiete , vol. 30, pp. 65–86, 1974
1974
Earlier work this paper cites.
M. L. Hautus, “A simple proof of Heymann’s lemma,” Automatic Control, IEEE Trans. on , vol. 22, no. 5, pp. 885–886, 1977
1977
Earlier work this paper cites.
A. Hotz and R. E. Skelton, “Covariance control theory,” International Journal of Control , vol. 46, no. 1, pp. 13–32, 1987
1987
Earlier work this paper cites.
A. Wakolbinger, “Schrödinger bridges from 1931 to 1991,” in Proc. of the 4th Latin American Congress in Probability and Mathematical Statistics, Mexico City , 1990, pp. 61–79
1990
Cited alongside, same era.
P. Dai Pra, “A stochastic control approach to reciprocal diffusion processes,” Applied mathematics and Optimization , vol. 23, no. 1, pp. 313–329, 1991
1991
Cited alongside, same era.
A. Beghi, “Continuous-time gauss-markov processes with fixed reciprocal dynamics,” Journal of Mathematical Systems Estimation and Control , vol. 7, pp. 343–366, 1997
1997
Cited alongside, same era.
S. Rowan and J. Hough, “Gravitational wave detection by interferometry (ground and space),” Living Rev. Relativity , vol. 3, no. 3, 2000
2000
Cited alongside, same era.
N. C. Petroni, S. De Martino, S. De Siena, and F. Illuminati, “Stochastic collective dynamics of charged-particle beams in the stability regime,” Physical Review E , vol. 63, no. 1, p. 016501, 2000
Y. Braiman, J. Barhen, and V. Protopopescu, “Control of friction at the nanoscale,” Physical Review Letters , vol. 90, no. 9, p. 094301, 2003
2003
Later among the works it cites.
A. Gannepalli, A. Sebastian, J. Cleveland, and M. Salapaka, “Thermally driven non-contact atomic force microscopy,” Applied Physics Letters , vol. 87, no. 11, p. 111901, 2005
2005
Later among the works it cites.
S. Toyabe, T. Okamoto, T. Watanabe-Nakayama, H. Taketani, S. Kudo, and E. Muneyuki, “Nonequilibrium energetics of a single f1-atpase molecule,” Physical Review Letters , vol. 104, no. 19, p. 198103, 2010
2010
Later among the works it cites.
I. G. Vladimirov and I. R. Petersen, “Minimum relative entropy state transitions in linear stochastic systems: the continuous time case,” in Proceedings of 19th International Symposium on Mathematical Theory of Networks and Systems , 2010, pp. 51–58
2010
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2000
Cited alongside, same era.
M. A. Hayes, N. A. Polson, and A. A. Garcia, “Active control of dynamic supraparticle structures in microchannels,” Langmuir , vol. 17, no. 9, pp. 2866–2871, 2001
2001
Cited alongside, same era.
T. T. Georgiou, “The structure of state covariances and its relation to the power spectrum of the input,” Automatic Control, IEEE Trans. on , vol. 47, no. 7, pp. 1056–1066, 2002
2002
Cited alongside, same era.
T. T. Georgiou, “Spectral analysis based on the state covariance: the maximum entropy spectrum and linear fractional parametrization,” Automatic Control, IEEE Trans. on , vol. 47, no. 11, pp. 1811–1823, 2002
2002
Cited alongside, same era.
F. Ricci, “Low temperature and gravitation wave detectors,” in Advanced Interferometers and the Search for Gravitational Waves . Springer, 2014, pp. 363–387
2014
Closest in time.
2014
Closest in time.