Solving High-Dimensional Optimal Control Problems with Empirical Tensor Train Approximation

Mathias Oster
RWTH Aachen University
Institut of Geometry and Applied Mathematics

We display two approaches to solve finite horizon optimal control problems with Tensor Train approximation. First we solve the Bellman equation numerically by employing the Policy Iteration algorithm.
Second, we introduce a semiglobal optimal con- trol problem and use open loop methods on a feedback level. To overcome computational infeasability we use tensor trains and multi-polynomials, together with high-dimensional quadrature rules, e.g. Monte-Carlo. By controlling a destabilized version of viscous Burgers and a diffusion equation with unstable reaction term numerical evidence is given.

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