An adaptive multiscale method for real-time moving horizon optimization

In the present work we explore an adaptive discretization scheme for dynamic optimization problems formulated on moving horizons. The proposed method is embedded into a solution methodology where the dynamic optimization problem is approximated by a hierarchy of successively refined finite dimensional problems. Information on the solution of the coarser approximations is used to initialize the employed NLP solver and to construct a fully adaptive, problem dependent discretization where the finite dimensional spaces are spanned by biorthogonal wavelets arising from B-splines. We demonstrate exemplarily that the proposed strategy is capable to identify accurate discretization meshes which are more economical than uniform meshes with respect to the ratio of approximation quality vs. number of trial functions used.