Hermite kernel surrogates for the value function of high-dimensional nonlinear optimal control problems

• Published in: Advances in computational mathematics Vol. 50; no. 3
• Main Authors: Ehring, Tobias, Haasdonk, Bernard
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2024; Springer Nature B.V
• Subjects: Algorithms; Cholesky factorization; Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Feedback control; Finite element method; Interpolation; Mathematical and Computational Biology; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; MORe 2022; Nonlinear control; Numerical methods; Optimal control; Visualization; Kernel methods; 93C10; Hermite interpolation; 93C15; Optimal feedback control; 30C40; Surrogate modeling; 49N35; 93B52

Numerical methods for the optimal feedback control of high-dimensional dynamical systems typically suffer from the curse of dimensionality. In the current presentation, we devise a mesh-free data-based approximation method for the value function of optimal control problems, which partially mitigates...