Amirhossein Karimi, Tryphon T. Georgiou
Published 2020-11-02Version 1
This manuscript introduces a regression-type formulation for approximating the Perron-Frobenius Operator by relying on distributional snapshots of data. These snapshots may represent densities of particles. The Wasserstein metric is leveraged to define a suitable functional optimization in the space of distributions. The formulation allows seeking suitable dynamics so as to interpolate the distributional flow in function space. A first-order necessary condition for optimality is derived and utilized to construct a gradient flow approximating algorithm. The framework is exemplied with numerical simulations.
Data-driven approximation of control invariant set for linear system based on convex piecewise linear fitting
Data-driven approximation for feasible regions in nonlinear model predictive control
Decomposition Algorithm for Distributionally Robust Optimization using Wasserstein Metric
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