Parallel Learning of Koopman Eigenfunctions and Invariant Subspaces for Accurate Long-Term Prediction
| Autor: | Jorge E. Cortes, Masih Haseli |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Control and Optimization
Computer Networks and Communications Intersection (set theory) Computer science Linear subspace Control and Systems Engineering Robustness (computer science) Signal Processing Graph (abstract data type) Invariant (mathematics) Dynamical system (definition) Communication complexity Algorithm Subspace topology |
| Zdroj: | IEEE Transactions on Control of Network Systems. 8:1833-1845 |
| ISSN: | 2372-2533 |
| Popis: | We present a parallel data-driven strategy to identify finite-dimensional functional spaces invariant under the Koopman operator associated to an unknown dynamical system. We build on the Symmetric Subspace Decomposition (SSD) algorithm, a centralized method that under mild conditions on data sampling provably finds the maximal Koopman-invariant subspace and all Koopman eigenfunctions in an arbitrary finite-dimensional functional space. A network of processors, each aware of a common dictionary of functions and equipped with a local set of data snapshots, repeatedly interact over a directed communication graph. Each processor receives its neighbors' estimates of the invariant dictionary and refines its estimate by applying SSD with its local data on the intersection of the subspaces spanned by its own dictionary and the neighbors' dictionaries. We identify conditions on the network topology to ensure the algorithm identifies the maximal Koopman-invariant subspace in the span of the original dictionary, characterize its time, computational, and communication complexity, and establish its robustness against communication failures. |
| Databáze: | OpenAIRE |
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