Fetching the paper…
Reading the bibliography…
We consider the continuous-time Linear-Quadratic-Regulator (LQR) problem in terms of optimizing a real-valued matrix function over the set of feedback gains.
R. E. Kalman, “Contributions to the theory of optimal control,” Boletinde la Sociedad Matematica Mexicana , vol. 5, no. 1, pp. 102–119, 1960
1960
Earlier work this paper cites.
B. T. Polyak, “Gradient methods for the minimisation of functionals,” USSR Computational Mathematics and Mathematical Physics , vol. 3, no. 4, pp. 864–878, 1963
1963
Earlier work this paper cites.
D. Kleinman and M. Athans, “The design of suboptimal linear time-varying systems,” IEEE Transactions on Automatic Control , vol. 13, no. 2, pp. 150–159, 1968
1968
Earlier work this paper cites.
D. Kleinman, “On an iterative technique for riccati equation computations,” IEEE Transactions on Automatic Control , vol. 13, no. 1, pp. 114–115, 1968
1968
Earlier work this paper cites.
W. Levine and M. Athans, “On the determination of the optimal constant output feedback gains for linear multivariable systems,” IEEE Transactions on Automatic control , vol. 15, no. 1, pp. 44–48, 1970
1970
Earlier work this paper cites.
G. Hewer, “An iterative technique for the computation of the steady state gains for the discrete optimal regulator,” IEEE Transactions on Automatic Control , vol. 16, no. 4, pp. 382–384, 1971
1971
Earlier work this paper cites.
W. Levine, T. Johnson, and M. Athans, “Optimal limited state variable feedback controllers for linear systems,” IEEE Transactions on Automatic Control , vol. 16, no. 6, pp. 785–793, 1971
1971
Earlier work this paper cites.
C. Knapp and S. Basuthakur, “On optimal output feedback,” IEEE Transactions on Automatic Control , vol. 17, no. 6, pp. 823–825, 1972
1972
Earlier work this paper cites.
C. Wenk and C. Knapp, “Parameter optimization in linear systems with arbitrarily constrained controller structure,” IEEE Transactions on Automatic Control , vol. 25, no. 3, pp. 496–500, 1980
1980
Earlier work this paper cites.
T. Mori, “Comments on" A matrix inequality associated with bounds on solutions of algebraic Riccati and Lyapunov equation" by J.M. Saniuk and I.B. Rhodes,” IEEE Transactions on Automatic Control , vol. 33, no. 11, p. 1088, 1988
1988
Earlier work this paper cites.
B. D. O. Anderson and J. B. Moore, Optimal Control: Linear Quadratic Methods . Upper Saddle River, NJ: Prentice-Hall, Inc., 1990
1990
Earlier work this paper cites.
S. J. Bradtke, B. E. Ydstie, and A. G. Barto, “Adaptive linear quadratic control using policy iteration,” in Proceedings of 1994 American Control Conference , vol. 3, 1994, pp. 3475–3479
1994
Cited alongside, same era.
P. Lancaster and L. Rodman, Algebraic Riccati Equations . New York, NY: Oxford University Press, 1995
1995
Cited alongside, same era.
V. Balakrishnan and L. Vandenberghe, “Semidefinite programming duality and linear time-invariant systems,” IEEE Transactions on Automatic Control , vol. 48, no. 1, pp. 30–41, 2003
2003
Cited alongside, same era.
Y. Nesterov, Introductory Lectures on Convex Optimization: A Basic Course . Springer Science & Business Media, 2004
2004
Cited alongside, same era.
R. A. Horn and C. R. Johnson, Matrix Analysis , 2nd ed. New York, NY: Cambridge University Press, 2012
2012
Later among the works it cites.
U. Helmke and J. B. Moore, Optimization and dynamical systems . Springer Science & Business Media, 2012
2012
Later among the works it cites.
M. Jilg and O. Stursberg, “Optimized distributed control and topology design for hierarchically interconnected systems,” in Control Conference (ECC), 2013 European . IEEE, 2013, pp. 4340–4346
2013
Later among the works it cites.
E. D. Sontag, Mathematical Control Theory: Deterministic Finite Dimensional Systems . Springer Science & Business Media, 2013, vol. 6
2013
Later among the works it cites.
T. Y. Chun, J. Y. Lee, J. B. Park, and Y. H. Choi, “Stability and monotone convergence of generalised policy iteration for discrete-time linear quadratic regulations,” International Journal of Control , vol. 89, no. 3, pp. 437–450, 2016
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2006
Cited alongside, same era.
F. L. Lewis and D. Vrabie, “Reinforcement learning and adaptive dynamic programming for feedback control,” IEEE Circuits and Systems Magazine , vol. 9, no. 3, pp. 32–50, 2009
2009
Cited alongside, same era.
K. Mårtensson and A. Rantzer, “Gradient methods for iterative distributed control synthesis,” in Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on . IEEE, 2009, pp. 549–554
2009
Cited alongside, same era.
Y. Jiang and Z.-P. Jiang, “Computational adaptive optimal control for continuous-time linear systems with completely unknown dynamics,” Automatica , vol. 48, no. 10, pp. 2699–2704, 2012
2012
Cited alongside, same era.
J. Y. Lee, J. B. Park, and Y. H. Choi, “Integral Q-learning and explorized policy iteration for adaptive optimal control of continuous-time linear systems,” Automatica , vol. 48, no. 11, pp. 2850–2859, 2012
2012
Cited alongside, same era.
F. L. Lewis, D. Vrabie, and K. G. Vamvoudakis, “Reinforcement learning and feedback control: using natural decision methods to design optimal adaptive controllers,” IEEE Control Systems , vol. 32, no. 6, pp. 76–105, 2012
2012
Cited alongside, same era.
K. Mårtensson, “Gradient methods for large-scale and distributed linear quadratic control,” Ph.D. dissertation, Department of Automatic Control, Lund University, Sweden, 2012
2012
Cited alongside, same era.
J. Bu, A. Mesbahi, and M. Mesbahi, “Lqr calculus,” preprint
Cited in the paper.
2016
Later among the works it cites.
L. W. Tu, Differential geometry: connections, curvature, and characteristic classes . Springer, 2017, vol. 275
2017
Later among the works it cites.
M. Fazel, R. Ge, S. Kakade, and M. Mesbahi, “Global convergence of policy gradient methods for the linear quadratic regulator,” in Proceedings of the 35th International Conference on Machine Learning , 2018, pp. 1467–1476
2018
Later among the works it cites.
2019
Later among the works it cites.
D. Lee and J. Hu, “Primal-dual Q-learning framework for LQR design,” IEEE Transactions on Automatic Control , 2019
2019
Later among the works it cites.
2019
Later among the works it cites.