HJB-RBF Based Approach for the Control of PDEs

[1]  Christian A. Glusa,et al.  Control of Fractional Diffusion Problems via Dynamic Programming Equations , 2022, Journal of Peridynamics and Nonlocal Modeling.

[2]  S. Dolgov,et al.  Data-driven Tensor Train Gradient Cross Approximation for Hamilton-Jacobi-Bellman Equations , 2022, SIAM J. Sci. Comput..

[3]  B. Haasdonk,et al.  Feedback control for coupled systems by kernel surrogates. , 2021, 9th edition of the International Conference on Computational Methods for Coupled Problems in Science and Engineering.

[4]  Alessandro Alla,et al.  A HJB-POD approach for the control of nonlinear PDEs on a tree structure , 2019, Applied Numerical Mathematics.

[5]  Maurizio Falcone,et al.  An Efficient DP Algorithm on a Tree-Structure for Finite Horizon Optimal Control Problems , 2018, SIAM J. Sci. Comput..

[6]  G. Ferretti,et al.  An adaptive multilevel radial basis function scheme for the HJB equation , 2017 .

[7]  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..

[8]  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.

[9]  Roberto Ferretti,et al.  A semi-Lagrangian scheme with radial basis approximation for surface reconstruction , 2016, Comput. Vis. Sci..

[10]  Stefan Volkwein,et al.  Error Analysis for POD Approximations of Infinite Horizon Problems via the Dynamic Programming Approach , 2015, SIAM J. Control. Optim..

[11]  Karen Willcox,et al.  A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems , 2015, SIAM Rev..

[12]  Gregory E. Fasshauer,et al.  Kernel-based Approximation Methods using MATLAB , 2015, Interdisciplinary Mathematical Sciences.

[13]  Bengt Fornberg,et al.  Solving PDEs with radial basis functions * , 2015, Acta Numerica.

[14]  O. Junge,et al.  Dynamic programming using radial basis functions , 2014, 1405.4002.

[15]  M. Falcone,et al.  Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations , 2014 .

[16]  Wen Chen,et al.  Recent Advances in Radial Basis Function Collocation Methods , 2013 .

[17]  Alessandro Alla,et al.  An Efficient Policy Iteration Algorithm for Dynamic Programming Equations , 2013, SIAM J. Sci. Comput..

[18]  Michael Griebel,et al.  An Adaptive Sparse Grid Semi-Lagrangian Scheme for First Order Hamilton-Jacobi Bellman Equations , 2012, Journal of Scientific Computing.

[19]  William M. McEneaney,et al.  Convergence Rate for a Curse-of-dimensionality-Free Method for Hamilton--Jacobi--Bellman PDEs Represented as Maxima of Quadratic Forms , 2009, SIAM J. Control. Optim..

[20]  William M. McEneaney,et al.  A Curse-of-Dimensionality-Free Numerical Method for Solution of Certain HJB PDEs , 2007, SIAM J. Control. Optim..

[21]  Randall J. LeVeque,et al.  Finite difference methods for ordinary and partial differential equations - steady-state and time-dependent problems , 2007 .

[22]  Gregory E. Fasshauer,et al.  Meshfree Approximation Methods with Matlab , 2007, Interdisciplinary Mathematical Sciences.

[23]  Maurizio Falcone,et al.  An efficient algorithm for Hamilton–Jacobi equations in high dimension , 2004 .

[24]  M. Bardi,et al.  Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations , 1997 .

[25]  Holger Wendland,et al.  Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree , 1995, Adv. Comput. Math..

[26]  Marizio Falcone,et al.  Discrete time high-order schemes for viscosity solutions of Hamilton-Jacobi-Bellman equations , 1994 .

[27]  H. Ishii,et al.  Approximate solutions of the bellman equation of deterministic control theory , 1984 .

[28]  I. Dolcetta On a discrete approximation of the Hamilton-Jacobi equation of dynamic programming , 1983 .

[29]  B. Haasdonk,et al.  Greedy sampling and approximation for realizing feedback control for high dimensional nonlinear systems , 2022, IFAC-PapersOnLine.

[30]  B. Haasdonk,et al.  FEEDBACK CONTROL FOR A COUPLED SOFT TISSUE SYSTEM BY KERNEL SURROGATES , 2021 .

[31]  Christian M. Chilan,et al.  Optimal Nonlinear Control Using Hamilton–Jacobi–Bellman Viscosity Solutions on Unstructured Grids , 2020 .

[32]  Bernard Haasdonk,et al.  Data-driven surrogates of value functions and applications to feedback control for dynamical systems , 2018 .

[33]  Jochen Garcke,et al.  Suboptimal Feedback Control of PDEs by Solving HJB Equations on Adaptive Sparse Grids , 2017, J. Sci. Comput..

[34]  M. Urner Scattered Data Approximation , 2016 .

[35]  S. Osher,et al.  Splitting Enables Overcoming the Curse of Dimensionality , 2016 .

[36]  Lei Xie,et al.  HJB-POD-Based Feedback Design for the Optimal Control of Evolution Problems , 2004, SIAM J. Appl. Dyn. Syst..

[37]  L. Grüne An adaptive grid scheme for the discrete Hamilton-Jacobi-Bellman equation , 1997 .