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Polynomial approximation of high-dimensional Hamilton–Jacobi–Bellman equations and applications to feedback control of semilinear parabolic PDES

Kalise, Dante; Kunisch, Karl

Authors

Karl Kunisch



Abstract

© 2018 Society for Industrial and Applied Mathematics. A procedure for the numerical approximation of high-dimensional Hamilton–Jacobi–Bellman (HJB) equations associated to optimal feedback control problems for semilinear parabolic equations is proposed. Its main ingredients are a pseudospectral collocation approximation of the PDE dynamics and an iterative method for the nonlinear HJB equation associated to the feedback synthesis. The latter is known as the successive Galerkin approximation. It can also be interpreted as Newton iteration for the HJB equation. At every step, the associated linear generalized HJB equation is approximated via a separable polynomial approximation ansatz. Stabilizing feedback controls are obtained from solutions to the HJB equations for systems of dimension up to fourteen.

Journal Article Type Article
Publication Date Jan 1, 2018
Journal SIAM Journal on Scientific Computing
Print ISSN 1064-8275
Electronic ISSN 1095-7197
Publisher Society for Industrial and Applied Mathematics
Peer Reviewed Peer Reviewed
Volume 40
Issue 2
Pages A629-A652
APA6 Citation Kalise, D., & Kunisch, K. (2018). Polynomial approximation of high-dimensional Hamilton–Jacobi–Bellman equations and applications to feedback control of semilinear parabolic PDES. SIAM Journal on Scientific Computing, 40(2), A629-A652. https://doi.org/10.1137/17M1116635
DOI https://doi.org/10.1137/17M1116635
Keywords Applied Mathematics; Computational Mathematics
Publisher URL https://epubs.siam.org/doi/10.1137/17M1116635

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