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In this paper, we propose an efficient numerical method to solve highdi...
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Approximating optimal feedback controllers of finite horizon control problems using hierarchical tensor formats
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Statedependent Riccati equation feedback stabilization for nonlinear PDEs
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Committor functions via tensor networks
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Gradientaugmented Supervised Learning of Optimal Feedback Laws Using Statedependent Riccati Equations
A supervised learning approach for the solution of largescale nonlinear...
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On the Adimensional Scale Invariant Steffensen (ASIS) Method
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Adaptive Deep Learning for High Dimensional HamiltonJacobiBellman Equations
Computing optimal feedback controls for nonlinear systems generally requ...
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A Tensor Decomposition Approach for HighDimensional HamiltonJacobiBellman Equations
A tensor decomposition approach for the solution of highdimensional, fully nonlinear HamiltonJacobiBellman equations arising in optimal feedback control and estimation of nonlinear dynamics is presented. The proposed method combines a tensor train approximation for the value function together with a Newtonlike iterative method for the solution of the resulting nonlinear system. The effectiveness of tensor approximations circumvents the curse of dimensionality, solving HamiltonJacobi equations with more than 100 dimensions at modest cost. The linear scaling of the computational complexity with respect to the dimension allows to solve PDEconstrained optimal feedback control problems over highdimensional state spaces. Numerical tests including the control of a 2D nonlinear reaction equation and the stabilization of a bilinear FokkerPlanck equation are presented.
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