 Approximation of optimal control problems for the Navier-Stokes equation via multilinear HJB-PODMaurizio Falcone, Gerhard Kirsten and Luca Saluzzi Applied Mathematics and Computation, 2023, vol. 442, issue C Abstract: We consider the approximation of some optimal control problems for the Navier-Stokes equation via a Dynamic Programming approach. These control problems arise in many industrial applications and are very challenging from the numerical point of view since the semi-discretization of the dynamics corresponds to an evolutive system of ordinary differential equations in very high-dimension. The typical approach is based on the Pontryagin maximum principle and leads to a two point boundary value problem. Here we present a different approach based on the value function and the solution of a Bellman equation, a challenging problem in high-dimension. We mitigate the curse of dimensionality via a recent multilinear approximation of the dynamics coupled with a dynamic programming scheme on a tree structure. We discuss several aspects related to the implementation of this new approach and we present some numerical examples to illustrate the results on classical control problems studied in the literature. Keywords: Dynamic programming; Optimal control; Tree structure; Model order reduction (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:442:y:2023:i:c:s0096300322007901 DOI: 10.1016/j.amc.2022.127722 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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