{"paper":{"title":"Koopman--Nemytskii Operator of Nonlinear Controlled Systems and Its Learning for Controller Synthesis","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.SY"],"primary_cat":"eess.SY","authors_text":"Wentao Tang","submitted_at":"2025-03-24T01:27:11Z","abstract_excerpt":"While the Koopman operator represents a nonlinear system as a linear operator in a function space, its definition does not involve inputs. For controller synthesis, an operator model is needed to describe the effect of feedback laws on closed-loop systems, so that the desired state-feedback law can be computationally searched based on such a predictive model. To this end, this paper proposes a Koopman--Nemytskii operator, defined as a linear operator that maps canonical features of state--policy pairs in a reproducing kernel Hilbert space (RKHS) to that of succeeding states. Under regularity c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.18269","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.18269/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}