Blog
About

12
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

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

      Preprint

      ,

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          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.

          Related collections

          Most cited references 19

          • Record: found
          • Abstract: not found
          • Article: not found

          A Markovian Decision Process

            Bookmark
            • Record: found
            • Abstract: not found
            • Article: not found

            Galerkin approximations of the generalized Hamilton-Jacobi-Bellman equation

              Bookmark
              • Record: found
              • Abstract: not found
              • Article: not found

              Some Convergence Results for Howard's Algorithm

                Bookmark

                Author and article information

                Journal
                2017-02-14
                Article
                1702.04400

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                math.OC math.NA

                Numerical & Computational mathematics, Numerical methods

                Comments

                Comment on this article