Lax-Oleinik-type formulas and efficient algorithms for certain high-dimensional optimal control problems
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[1] Masayoshi Tomizuka,et al. Autonomous Driving Motion Planning With Constrained Iterative LQR , 2019, IEEE Transactions on Intelligent Vehicles.
[2] James E. Bobrow,et al. An efficient sequential linear quadratic algorithm for solving nonlinear optimal control problems , 2005, Proceedings of the 2005, American Control Conference, 2005..
[3] Jochen Garcke,et al. Suboptimal Feedback Control of PDEs by Solving HJB Equations on Adaptive Sparse Grids , 2017, J. Sci. Comput..
[4] Scott Kuindersma,et al. An Architecture for Online Affordance‐based Perception and Whole‐body Planning , 2015, J. Field Robotics.
[5] W.M. McEneaney,et al. Curse-of-complexity attenuation in the curse-of-dimensionality-free method for HJB PDEs , 2008, 2008 American Control Conference.
[6] Chi-Wang Shu,et al. A Discontinuous Galerkin Finite Element Method for Hamilton-Jacobi Equations , 1999, SIAM J. Sci. Comput..
[7] Maurizio Falcone,et al. An Efficient DP Algorithm on a Tree-Structure for Finite Horizon Optimal Control Problems , 2018, SIAM J. Sci. Comput..
[8] Samy Wu Fung,et al. A Neural Network Approach for High-Dimensional Optimal Control , 2021, 2104.03270.
[9] Tingwei Meng,et al. On some neural network architectures that can represent viscosity solutions of certain high dimensional Hamilton-Jacobi partial differential equations , 2021, J. Comput. Phys..
[10] George Em Karniadakis,et al. SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems , 2020, Neural Networks.
[11] Frank L. Lewis,et al. Intelligent optimal control of robotic manipulators using neural networks , 2000, Autom..
[12] B. Kouvaritakis,et al. Efficient MPC Optimization using Pontryagin's Minimum Principle , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.
[13] William M. McEneaney,et al. Max-plus methods for nonlinear control and estimation , 2005 .
[14] Richard Bellman,et al. Adaptive Control Processes: A Guided Tour , 1961, The Mathematical Gazette.
[15] Somil Bansal,et al. Generating Robust Supervision for Learning-Based Visual Navigation Using Hamilton-Jacobi Reachability , 2020, L4DC.
[16] Huan Zhang,et al. Max-plus fundamental solution semigroups for optimal control problems , 2015, SIAM Conf. on Control and its Applications.
[17] Masayoshi Tomizuka,et al. Alternating Direction Method of Multipliers for Constrained Iterative LQR in Autonomous Driving , 2020, ArXiv.
[18] Wei Zhan,et al. Constrained iterative LQR for on-road autonomous driving motion planning , 2017, 2017 IEEE 20th International Conference on Intelligent Transportation Systems (ITSC).
[19] Danping Peng,et al. Weighted ENO Schemes for Hamilton-Jacobi Equations , 1999, SIAM J. Sci. Comput..
[20] Stéphane Gaubert,et al. The Max-Plus Finite Element Method for Solving Deterministic Optimal Control Problems: Basic Properties and Convergence Analysis , 2008, SIAM J. Control. Optim..
[21] Frank L. Lewis,et al. Robot Manipulator Control: Theory and Practice , 2003 .
[22] Justin A. Sirignano,et al. DGM: A deep learning algorithm for solving partial differential equations , 2017, J. Comput. Phys..
[23] Somil Bansal,et al. DeepReach: A Deep Learning Approach to High-Dimensional Reachability , 2020, 2021 IEEE International Conference on Robotics and Automation (ICRA).
[24] K. G. Farlow,et al. Max-Plus Algebra , 2009 .
[25] J. Lygeros,et al. Neural approximation of PDE solutions: An application to reachability computations , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.
[26] Marceau Coupechoux,et al. Optimal Trajectories of a UAV Base Station Using Lagrangian Mechanics , 2018, IEEE INFOCOM 2019 - IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS).
[27] Jianfeng Lu,et al. Actor-Critic Method for High Dimensional Static Hamilton-Jacobi-Bellman Partial Differential Equations based on Neural Networks , 2021, SIAM J. Sci. Comput..
[28] Roland Glowinski,et al. On Alternating Direction Methods of Multipliers: A Historical Perspective , 2014, Modeling, Simulation and Optimization for Science and Technology.
[29] Jérôme Darbon,et al. On Convex Finite-Dimensional Variational Methods in Imaging Sciences and Hamilton-Jacobi Equations , 2015, SIAM J. Imaging Sci..
[30] C. Yalçin Kaya,et al. A Duality Approach for Solving Control-Constrained Linear-Quadratic Optimal Control Problems , 2014, SIAM J. Control. Optim..
[31] J. Denk,et al. Synthesis of a Walking Primitive Database for a Humanoid Robot using Optimal Control Techniques , 2001 .
[32] Qi Gong,et al. QRnet: Optimal Regulator Design With LQR-Augmented Neural Networks , 2020, IEEE Control Systems Letters.
[33] H. Pham,et al. Deep neural networks algorithms for stochastic control problems on finite horizon, part I: convergence analysis , 2020 .
[34] Daniel Delahaye,et al. (EN-023) Mathematical Models for Aircraft Trajectory Design : A Survey. , 2013 .
[35] Wook Hyun Kwon,et al. LQ tracking controls with fixed terminal states and their application to receding horizon controls , 2008, Syst. Control. Lett..
[36] Mo Chen,et al. Reachability-Based Safety and Goal Satisfaction of Unmanned Aerial Platoons on Air Highways , 2016, 1602.08150.
[37] Shuai Li,et al. Robot manipulator control using neural networks: A survey , 2018, Neurocomputing.
[38] S. Puechmorel,et al. On a Hamilton‐Jacobi‐Bellman approach for coordinated optimal aircraft trajectories planning , 2016 .
[39] Wotao Yin,et al. Faster Convergence Rates of Relaxed Peaceman-Rachford and ADMM Under Regularity Assumptions , 2014, Math. Oper. Res..
[40] William M. McEneaney,et al. A Max-Plus-Based Algorithm for a Hamilton--Jacobi--Bellman Equation of Nonlinear Filtering , 2000, SIAM J. Control. Optim..
[41] Arnulf Jentzen,et al. Solving high-dimensional partial differential equations using deep learning , 2017, Proceedings of the National Academy of Sciences.
[42] Stefan Volkwein,et al. Error Analysis for POD Approximations of Infinite Horizon Problems via the Dynamic Programming Approach , 2015, SIAM J. Control. Optim..
[43] Peter M. Dower,et al. Neural network architectures using min plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs , 2021, ArXiv.
[44] Tingwei Meng,et al. Overcoming the curse of dimensionality for some Hamilton–Jacobi partial differential equations via neural network architectures , 2019 .
[45] William M. McEneaney,et al. Convergence Rate for a Curse-of-Dimensionality-Free Method for a Class of HJB PDEs , 2009, SIAM J. Control. Optim..
[46] Feng Lin,et al. An optimal control approach to robust control of robot manipulators , 1998, IEEE Trans. Robotics Autom..
[47] Shuuji Kajita,et al. An optimal planning of falling motions of a humanoid robot , 2007, 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems.
[48] Zhen Zhang,et al. Learning Poisson systems and trajectories of autonomous systems via Poisson neural networks , 2020, ArXiv.
[49] Claire J. Tomlin,et al. A Hopf-Lax Formula in Hamilton–Jacobi Analysis of Reach-Avoid Problems , 2021, IEEE Control Systems Letters.
[50] William M. McEneaney,et al. A Curse-of-Dimensionality-Free Numerical Method for Solution of Certain HJB PDEs , 2007, SIAM J. Control. Optim..
[51] Hussein Jaddu,et al. Spectral method for constrained linear-quadratic optimal control , 2002, Math. Comput. Simul..
[52] Wei Kang,et al. Mitigating the curse of dimensionality: sparse grid characteristics method for optimal feedback control and HJB equations , 2015, Computational Optimization and Applications.
[53] Scott Kuindersma,et al. Optimization-based locomotion planning, estimation, and control design for the atlas humanoid robot , 2015, Autonomous Robots.
[54] Huyên Pham,et al. Some machine learning schemes for high-dimensional nonlinear PDEs , 2019, ArXiv.
[55] J. Lygeros,et al. A Neural Approximation to Continuous Time Reachability Computations , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.
[56] Florent Lamiraux,et al. Optimal motion planning for humanoid robots , 2013, 2013 IEEE International Conference on Robotics and Automation.
[57] Joel W. Burdick,et al. Linear Hamilton Jacobi Bellman Equations in high dimensions , 2014, 53rd IEEE Conference on Decision and Control.
[58] Alessandro Rucco,et al. Optimal Rendezvous Trajectory for Unmanned Aerial-Ground Vehicles , 2018, IEEE Transactions on Aerospace and Electronic Systems.
[59] Stephen P. Boyd,et al. Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..
[60] Michael Muehlebach,et al. Application of an approximate model predictive control scheme on an unmanned aerial vehicle , 2016, 2016 IEEE International Conference on Robotics and Automation (ICRA).
[61] Michael Griebel,et al. An Adaptive Sparse Grid Semi-Lagrangian Scheme for First Order Hamilton-Jacobi Bellman Equations , 2012, Journal of Scientific Computing.
[62] Emanuel Todorov,et al. Iterative Linear Quadratic Regulator Design for Nonlinear Biological Movement Systems , 2004, ICINCO.
[63] S. Osher,et al. Algorithms for overcoming the curse of dimensionality for certain Hamilton–Jacobi equations arising in control theory and elsewhere , 2016, Research in the Mathematical Sciences.
[64] M. Bardi,et al. Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations , 1997 .
[65] Karl Kunisch,et al. Robust Feedback Control of Nonlinear PDEs by Numerical Approximation of High-Dimensional Hamilton-Jacobi-Isaacs Equations , 2019, SIAM J. Appl. Dyn. Syst..
[66] D. Bertsekas. Reinforcement Learning and Optimal ControlA Selective Overview , 2018 .
[67] Christoph Reisinger,et al. Rectified deep neural networks overcome the curse of dimensionality for nonsmooth value functions in zero-sum games of nonlinear stiff systems , 2019, Analysis and Applications.
[68] William M. McEneaney,et al. Curse of dimensionality reduction in max-plus based approximation methods: Theoretical estimates and improved pruning algorithms , 2011, IEEE Conference on Decision and Control and European Control Conference.
[69] Karl Kunisch,et al. Polynomial Approximation of High-Dimensional Hamilton-Jacobi-Bellman Equations and Applications to Feedback Control of Semilinear Parabolic PDEs , 2017, SIAM J. Sci. Comput..
[70] Claire J. Tomlin,et al. A Computationally Efficient Hamilton-Jacobi-based Formula for State-Constrained Optimal Control Problems , 2021, ArXiv.
[71] Tingwei Meng,et al. On Decomposition Models in Imaging Sciences and Multi-time Hamilton-Jacobi Partial Differential Equations , 2019, SIAM J. Imaging Sci..
[72] Lei Xie,et al. HJB-POD-Based Feedback Design for the Optimal Control of Evolution Problems , 2004, SIAM J. Appl. Dyn. Syst..
[73] Wang Hai-bing,et al. High-order essentially non-oscillatory schemes for Hamilton-Jacobi equations , 2006 .
[74] Christopher G. Atkeson,et al. Optimization based full body control for the atlas robot , 2014, 2014 IEEE-RAS International Conference on Humanoid Robots.
[75] Emanuel Todorov,et al. Efficient computation of optimal actions , 2009, Proceedings of the National Academy of Sciences.
[76] Wotao Yin,et al. On the Global and Linear Convergence of the Generalized Alternating Direction Method of Multipliers , 2016, J. Sci. Comput..