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We consider the problem to steer a linear dynamical system with full state observation from an initial gaussian distribution in state-space to a final one with minimum energy control.
E. Nelson, Dynamical theories of Brownian motion . Princeton university press Princeton, 1967, vol. 17
1967
Earlier work this paper cites.
W. H. Fleming, Logarithmic transformations and stochastic control . Springer, 1982
1982
Earlier work this paper cites.
W. H. Fleming and R. Rishel, Deterministic and Stochastic Optimal Control (Stochastic Modelling and Applied Probability) . Springer, 1982
1982
Earlier work this paper cites.
M. Doi, The theory of polymer dynamics . Oxford University Press, 1988, no. 73
1988
Earlier work this paper cites.
H. Föllmer, “Random fields and diffusion processes,” in École d’Été de Probabilités de Saint-Flour XV–XVII, 1985–87 . Springer, 1988, pp. 101–203
1988
Earlier work this paper cites.
A. Wakolbinger, “A simplified variational characterization of Schrödinger processes,” Journal of mathematical physics , vol. 30, no. 12, pp. 2943–2946, 1989
1989
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
Earlier work this paper cites.
P. Dai Pra and M. Pavon, “On the Markov processes of Schrödinger, the Feynman-Kac formula and stochastic control,” in Realization and Modelling in System Theory . Springer, 1990, pp. 497–504
1990
Earlier work this paper cites.
P. Dai Pra, “A stochastic control approach to reciprocal diffusion processes,” Applied mathematics and Optimization , vol. 23, no. 1, pp. 313–329, 1991
1991
Earlier work this paper cites.
M. Pavon and A. Wakolbinger, “On free energy, stochastic control, and Schrödinger processes,” in Modeling, Estimation and Control of Systems with Uncertainty . Springer, 1991, pp. 334–348
1991
Cited alongside, same era.
B. C. Levy and A. J. Krener, “Dynamics and kinematics of reciprocal diffusions,” Journal of mathematical physics , vol. 34, no. 5, pp. 1846–1875, 1993
1993
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.
K. M. Grigoriadis and R. E. Skelton, “Minimum-energy covariance controllers,” Automatica , vol. 33, no. 4, pp. 569–578, 1997
1997
Cited alongside, same era.
S. Liang, D. Medich, D. M. Czajkowsky, S. Sheng, J.-Y. Yuan, and Z. Shao, “Thermal noise reduction of mechanical oscillators by actively controlled external dissipative forces,” Ultramicroscopy , vol. 84, no. 1, pp. 119–125, 2000
A. Vinante, M. Bignotto, M. Bonaldi, M. Cerdonio, L. Conti, P. Falferi, N. Liguori, S. Longo, R. Mezzena, A. Ortolan et al. , “Feedback cooling of the normal modes of a massive electromechanical system to submillikelvin temperature,” Physical review letters , vol. 101, no. 3, p. 033601, 2008
2008
Later among the works it cites.
R. Filliger, M.-O. Hongler, and L. Streit, “Connection between an exactly solvable stochastic optimal control problem and a nonlinear reaction-diffusion equation,” Journal of Optimization Theory and Applications , vol. 137, no. 3, pp. 497–505, 2008
2008
Later among the works it cites.
M. Bonaldi, L. Conti, P. De Gregorio, L. Rondoni, G. Vedovato, A. Vinante, M. Bignotto, M. Cerdonio, P. Falferi, N. Liguori et al. , “Nonequilibrium steady-state fluctuations in actively cooled resonators,” Physical review letters , vol. 103, no. 1, p. 010601, 2009
2009
Later among the works it cites.
M. Pavon and F. Ticozzi, “Discrete-time classical and quantum Markovian evolutions: Maximum entropy problems on path space,” Journal of Mathematical Physics , vol. 51, no. 4, p. 042104, 2010
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2000
Cited alongside, same era.
J. Tamayo, A. Humphris, R. Owen, and M. Miles, “High dynamic force microscopy in liquid and its application to living cells,” Biophysical journal , vol. 81, no. 1, pp. 526–537, 2001
2001
Cited alongside, same era.
P. Reimann, “Brownian motors: noisy transport far from equilibrium,” Physics Reports , vol. 361, no. 2, pp. 57–265, 2002
2002
Cited alongside, same era.
Y. Braiman, J. Barhen, and V. Protopopescu, “Control of friction at the nanoscale,” Physical review letters , vol. 90, no. 9, p. 094301, 2003
2003
Cited alongside, same era.
R. Filliger and M.-O. Hongler, “Relative entropy and efficiency measure for diffusion-mediated transport processes,” Journal of Physics A: Mathematical and General , vol. 38, no. 6, p. 1247, 2005
2005
Cited alongside, same era.
Y. Chen, T. Georgiou, and P. Michele, “Steering of stochastic oscillators over a Schrödinger bridge,” in preparation
Cited in the paper.
2010
Later among the works it cites.
C. Altafini and F. Ticozzi, “Modeling and control of quantum systems: an introduction,” Automatic Control, IEEE Transactions on , vol. 57, no. 8, pp. 1898–1917, 2012
2012
Later among the works it cites.
M. Poot and H. S. van der Zant, “Mechanical systems in the quantum regime,” Physics Reports , vol. 511, no. 5, pp. 273–335, 2012
2012
Later among the works it cites.
2014
Closest in time.
2014
Closest in time.
P. Kosmol and M. Pavon, “Lagrange lemma and the optimal control of diffusion. 1. Differentiable multipliers,” in Proceedings of the 31st IEEE Conference on Decision and Control . IEEE, 1992, pp. 2037–2042
2042
Closest in time.