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A sparse regression approach for the computation of high-dimensional optimal feedback laws arising in deterministic nonlinear control is proposed.
Synthesis of control lyapunov functions and stabilizing feedback strategies using exit-time optimal control, 2019
I. Yegorov, P. M. Dower, and L. Grüne · 1906
Earlier work this paper cites.
Adaptive Deep Learning for High-Dimensional Hamilton-Jacobi-Bellman Equations, 2019
T. Nakamura-Zimmerer, Q. Gong, and W. Kang · 1907
Earlier work this paper cites.
Tensor Decompositions for High-dimensional Hamilton-Jacobi-Bellman Equations, 2019
S. Dolgov, D. Kalise, and K. Kunisch · 1908
Earlier work this paper cites.
Approximating the stationary Hamilton-Jacobi-Bellman equation by hierarchical tensor products, 2019
M. Oster, L. Sallandt, and R. Schneider · 1911
Earlier work this paper cites.
Algorithms of Data Development For Deep Learning and Feedback Design, 2019
W. Kang, Q. Gong, and T. Nakamura-Zimmerer · 1912
Earlier work this paper cites.
On the optimal stabilization of nonlinear systems
E. Al’brekht · 1961
Earlier work this paper cites.
Adaptive control processes: A guided tour
R. Bellman · 1961
Earlier work this paper cites.
The mathematical theory of optimal processes
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko · 1962
Earlier work this paper cites.
On the stability of the numerical integration of systems of ordinary differential equations arising in the use of the straight line method
E. Sarmin and L. Chudov · 1963
Earlier work this paper cites.
Optimal regulation of nonlinear dynamical systems
D. Lukes · 1969
Earlier work this paper cites.
The Pontryagin maximum principle from dynamic programming and viscosity solutions to first-order partial differential equations
E. N. Barron and R. Jensen · 1986
Earlier work this paper cites.
The relationship between the maximum principle and dynamic programming
F. H. Clarke and R. B. Vinter · 1987
Earlier work this paper cites.
Two-point step size gradient methods
J. Barzilai and J. M. Borwein · 1988
Earlier work this paper cites.
Some characterizations of optimal trajectories in control theory
P. Cannarsa and H. Frankowska · 1991
Earlier work this paper cites.
Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations
M. Bardi and I. Capuzzo-Dolcetta · 1997
Earlier work this paper cites.
Feedback control methodologies for nonlinear systems
S. C. Beeler, H. T. Tran, and H. T. Banks · 2000
Earlier work this paper cites.
The gap between theory and practice in function approximation with deep neural networks, 2020
B. Adcock and N. Dexter · 2001
Earlier work this paper cites.
Adaptive two-point stepsize gradient algorithm
Y.-H. Dai and H. Zhang · 2001
Earlier work this paper cites.
Reduced order feedback synthesis for viscous incompressible flows
K. Ito and J. Schroeter · 2001
Earlier work this paper cites.
Value function in optimal control
H. Frankowska · 2002
Earlier work this paper cites.
Semiglobal optimal feedback stabilization of autonomous systems via deep neural network approximation, 2020
K. Kunisch and D. Walter · 2002
Earlier work this paper cites.
Deep xVA solver – A neural network based counterparty credit risk management framework, 2020
A. Gnoatto, A. Picarelli, and C. Reisinger · 2005
Earlier work this paper cites.
Solving high-dimensional Hamilton-Jacobi-Bellman pdes using neural networks: perspectives from the theory of controlled diffusions and measures on path space, 2020
N. Nüsken and L. Richter · 2005
Earlier work this paper cites.
The method of characteristics for the Hamilton-Jacobi equations and its applications in dynamic optimization
N. N. Subbotina · 2006
Earlier work this paper cites.
Emergent behavior in flocks
F. Cucker and S. Smale · 2007
Earlier work this paper cites.
A curse-of-dimensionality-free numerical method for solution of certain HJB PDEs
W. M. McEneaney · 2007
Cited alongside, same era.
The max-plus finite element method for solving deterministic optimal control problems: basic properties and convergence analysis
M. Akian, S. Gaubert, and A. Lakhoua · 2008
Cited alongside, same era.
On the infinite horizon performance of receding horizon controllers
L. Grüne and A. Rantzer · 2008
Cited alongside, same era.
A Causality Free Computational Method for HJB Equations with Application to Rigid Body Satellites
W. Kang and L. Wilcox · 2009
Cited alongside, same era.
The maximum principle of optimal control: a history of ingenious ideas and missed opportunities
H. J. Pesch and M. Plail · 2009
Cited alongside, same era.
Initialization of the shooting method via the Hamilton-Jacobi-Bellman approach
First-order methods in optimization , volume 25 of MOS-SIAM Series on Optimization
A. Beck · 2017
Later among the works it cites.
Feedback stabilization to nonstationary solutions of a class of reaction diffusion equations of fitzhugh–nagumo type
T. Breiten, K. Kunisch, and S. S. Rodrigues · 2017
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Algorithm for overcoming the curse of dimensionality for time-dependent non-convex Hamilton-Jacobi equations arising from optimal control and differential games problems
Y. T. Chow, J. Darbon, S. Osher, and W. Yin · 2017
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Suboptimal feedback control of PDEs by solving HJB equations on adaptive sparse grids
J. Garcke and A. Kröner · 2017
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Mitigating the curse of dimensionality: sparse grid characteristics method for optimal feedback control and HJB equations
W. Kang and L. C. Wilcox · 2017
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E. Cristiani and P. Martinon · 2010
Cited alongside, same era.
Algorithms for PDE-constrained optimization
R. Herzog and K. Kunisch · 2010
Cited alongside, same era.
Distributed optimization and statistical learning via the alternating direction method of multipliers
S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein, et al · 2011
Cited alongside, same era.
Analytic regularity and polynomial approximation of parametric and stochastic elliptic PDE’s
A. Cohen, R. Devore, and C. Schwab · 2011
Cited alongside, same era.
On the optimal polynomial approximation of stochastic PDEs by Galerkin and collocation methods
J. Beck, R. Tempone, F. Nobile, and L. Tamellini · 2012
Cited alongside, same era.
Unconstrained model predictive control and suboptimality estimates for nonlinear continuous-time systems
M. Reble and F. Allgöwer · 2012
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An adaptive sparse grid semi-Lagrangian scheme for first order Hamilton-Jacobi Bellman equations
O. Bokanowski, J. Garcke, M. Griebel, and I. Klompmaker · 2013
Cited alongside, same era.
Optimal consensus control of the cucker-smale model
R. Bailo, M. Bongini, J. A. Carrillo, and D. Kalise · 2018
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Algorithm for overcoming the curse of dimensionality for certain non-convex Hamilton-Jacobi equations, projections and differential games
Y. T. Chow, J. Darbon, S. Osher, and W. Yin · 2018
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Mean field limits for interacting diffusions in a two-scale potential
S. N. Gomes and G. A. Pavliotis · 2018
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High-dimensional stochastic optimal control using continuous tensor decompositions
A. Gorodetsky, S. Karaman, and Y. Marzouk · 2018
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Solving high-dimensional partial differential equations using deep learning
J. Han, A. Jentzen, and W. E · 2018
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Polynomial approximation of high-dimensional Hamilton-Jacobi-Bellman equations and applications to feedback control of semilinear parabolic PDEs
D. Kalise and K. Kunisch · 2018
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Perspectives on Characteristics Based Curse-of-Dimensionality-Free Numerical Approaches for Solving Hamilton–Jacobi Equations
I. Yegorov and P. M. Dower · 2018
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Ann. Inst. H. Poincaré Anal. Non Linéaire , 36(5):1361 – 1399, 2019
Taylor expansions of the value function associated with a bilinear optimal control problem · 2019
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Compressive Hermite interpolation: sparse, high-dimensional approximation from gradient-augmented measurements
B. Adcock and Y. Sui · 2019
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Correcting for unknown errors in sparse high-dimensional function approximation
B. Adcock, A. Bao, and S. Brugiapaglia · 2019
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An efficient DP algorithm on a tree-structure for finite horizon optimal control problems
A. Alla, M. Falcone, and L. Saluzzi · 2019
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Reinforcement Learning and Optimal Control
D. P. Bertsekas · 2019
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A collisionless singular Cucker-Smale model with decentralized formation control
Y.-P. Choi, D. Kalise, J. Peszek, and A. A. Peters · 2019
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Algorithm for overcoming the curse of dimensionality for state-dependent Hamilton-Jacobi equations
Y. T. Chow, J. Darbon, S. Osher, and W. Yin · 2019
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An overview of gradient-enhanced metamodels with applications
L. Laurent, R. Le Riche, B. Soulier, and P.-A. Boucard · 2019
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Computing Lyapunov functions using deep neural networks, 2020
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Analysis of the Barzilai-Borwein step-sizes for problems in Hilbert spaces
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Overcoming the curse of dimensionality for some Hamilton-Jacobi partial differential equations via neural network architectures, 2020
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A neural network-based policy iteration algorithm with global h 2 h^{2} -superlinear convergence for stochastic games on domains
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Robust feedback control of nonlinear PDEs by numerical approximation of high-dimensional Hamilton-Jacobi-Isaacs equations
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