Intrinsic and Extrinsic Approximation of Koopman Operators over Manifolds
| Autor: | Sai Tej Paruchuri, Daniel J. Stilwell, Andrew J. Kurdila, Jia Guo, Tim Ryan, Haoran Wang, Michael E. Kepler |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Dynamical Systems (math.DS)
Numerical Analysis (math.NA) Systems and Control (eess.SY) 010103 numerical & computational mathematics Type (model theory) Electrical Engineering and Systems Science - Systems and Control 01 natural sciences Projection (linear algebra) Complete metric space Manifold 010305 fluids & plasmas Operator (computer programming) Optimization and Control (math.OC) Kernel (statistics) 0103 physical sciences Convergence (routing) FOS: Mathematics FOS: Electrical engineering electronic engineering information engineering Trajectory Applied mathematics Mathematics - Numerical Analysis Mathematics - Dynamical Systems 0101 mathematics Mathematics - Optimization and Control Mathematics |
| Zdroj: | CDC |
| DOI: | 10.1109/cdc42340.2020.9304383 |
| Popis: | This paper derives rates of convergence of certain approximations of the Koopman operators that are associated with discrete, deterministic, continuous semiflows on a complete metric space $(X,d_X)$. Approximations are constructed in terms of reproducing kernel bases that are centered at samples taken along the system trajectory. It is proven that when the samples are dense in a certain type of smooth manifold $M\subseteq X$, the derived rates of convergence depend on the fill distance of samples along the trajectory in that manifold. Error bounds for projection-based and data-dependent approximations of the Koopman operator are derived in the paper. A discussion of how these bounds are realized in intrinsic and extrinsic approximation methods is given. Finally, a numerical example that illustrates qualitatively the convergence guarantees derived in the paper is given. 8 pages, 5 figures, conference |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|