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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