{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:VTUIZWAKOJEYJDOGINU2XMJ7VG","short_pith_number":"pith:VTUIZWAK","canonical_record":{"source":{"id":"1810.00089","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-09-28T21:40:43Z","cross_cats_sorted":[],"title_canon_sha256":"2616da76fe32be906911aafc079a483f841aa9c1251c8eb2ed79aeb9eb210751","abstract_canon_sha256":"95ef2013b73c0ab9ab5738aad7ad7eb3e5e4e5f8d3d77ffd846e3c688e2c004a"},"schema_version":"1.0"},"canonical_sha256":"ace88cd80a7249848dc64369abb13fa9a48886091f09e8b2b8b5d0468a43b416","source":{"kind":"arxiv","id":"1810.00089","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.00089","created_at":"2026-05-18T00:04:28Z"},{"alias_kind":"arxiv_version","alias_value":"1810.00089v1","created_at":"2026-05-18T00:04:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00089","created_at":"2026-05-18T00:04:28Z"},{"alias_kind":"pith_short_12","alias_value":"VTUIZWAKOJEY","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VTUIZWAKOJEYJDOG","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VTUIZWAK","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:VTUIZWAKOJEYJDOGINU2XMJ7VG","target":"record","payload":{"canonical_record":{"source":{"id":"1810.00089","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-09-28T21:40:43Z","cross_cats_sorted":[],"title_canon_sha256":"2616da76fe32be906911aafc079a483f841aa9c1251c8eb2ed79aeb9eb210751","abstract_canon_sha256":"95ef2013b73c0ab9ab5738aad7ad7eb3e5e4e5f8d3d77ffd846e3c688e2c004a"},"schema_version":"1.0"},"canonical_sha256":"ace88cd80a7249848dc64369abb13fa9a48886091f09e8b2b8b5d0468a43b416","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:28.842983Z","signature_b64":"4g1eMl1e5nU1QytOAVu2A9IefvTyaRT500xXR7HrgXhr+UpoW/BrA2Ky3uHAuZk/7aIAxgeT72iPAp1Kok6AAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ace88cd80a7249848dc64369abb13fa9a48886091f09e8b2b8b5d0468a43b416","last_reissued_at":"2026-05-18T00:04:28.842352Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:28.842352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.00089","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:04:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p8qUDUWbgm4nVeK2jlNgmmQZuP3+4vKs5Unt6Nw0K0E7fOhB/k/4RRMWT0hjeb+6ggzNRwPCMVWkde/izykLCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:57:31.092908Z"},"content_sha256":"3d94748a0942d85128b4ad9d78bc3ace1a2ad2d1321fdc8166c149eee7820437","schema_version":"1.0","event_id":"sha256:3d94748a0942d85128b4ad9d78bc3ace1a2ad2d1321fdc8166c149eee7820437"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:VTUIZWAKOJEYJDOGINU2XMJ7VG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Feedback Stabilization Using Koopman Operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bowen Huang, Umesh Vaidya, Xu Ma","submitted_at":"2018-09-28T21:40:43Z","abstract_excerpt":"In this paper, we provide a systematic approach for the design of stabilizing feedback controllers for nonlinear control systems using the Koopman operator framework. The Koopman operator approach provides a linear representation for a nonlinear dynamical system and a bilinear representation for a nonlinear control system. The problem of feedback stabilization of a nonlinear control system is then transformed to the stabilization of a bilinear control system. We propose a control Lyapunov function (CLF)-based approach for the design of stabilizing feedback controllers for the bilinear system. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00089","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:04:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1jJk0YrZ6FrTUL/fPWf/mGdZ9lc06fSKHjUUf4S7l9p1irRHFZOzwEeaujjE0PPLJd6gJ5ZL6rtsVNMYgI83DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:57:31.093253Z"},"content_sha256":"65f4244f24e97ad1596bcde28cd95a3f55e82e93ab9d91c891aff8c9591132ed","schema_version":"1.0","event_id":"sha256:65f4244f24e97ad1596bcde28cd95a3f55e82e93ab9d91c891aff8c9591132ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VTUIZWAKOJEYJDOGINU2XMJ7VG/bundle.json","state_url":"https://pith.science/pith/VTUIZWAKOJEYJDOGINU2XMJ7VG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VTUIZWAKOJEYJDOGINU2XMJ7VG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T00:57:31Z","links":{"resolver":"https://pith.science/pith/VTUIZWAKOJEYJDOGINU2XMJ7VG","bundle":"https://pith.science/pith/VTUIZWAKOJEYJDOGINU2XMJ7VG/bundle.json","state":"https://pith.science/pith/VTUIZWAKOJEYJDOGINU2XMJ7VG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VTUIZWAKOJEYJDOGINU2XMJ7VG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VTUIZWAKOJEYJDOGINU2XMJ7VG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"95ef2013b73c0ab9ab5738aad7ad7eb3e5e4e5f8d3d77ffd846e3c688e2c004a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-09-28T21:40:43Z","title_canon_sha256":"2616da76fe32be906911aafc079a483f841aa9c1251c8eb2ed79aeb9eb210751"},"schema_version":"1.0","source":{"id":"1810.00089","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.00089","created_at":"2026-05-18T00:04:28Z"},{"alias_kind":"arxiv_version","alias_value":"1810.00089v1","created_at":"2026-05-18T00:04:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00089","created_at":"2026-05-18T00:04:28Z"},{"alias_kind":"pith_short_12","alias_value":"VTUIZWAKOJEY","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VTUIZWAKOJEYJDOG","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VTUIZWAK","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:65f4244f24e97ad1596bcde28cd95a3f55e82e93ab9d91c891aff8c9591132ed","target":"graph","created_at":"2026-05-18T00:04:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we provide a systematic approach for the design of stabilizing feedback controllers for nonlinear control systems using the Koopman operator framework. The Koopman operator approach provides a linear representation for a nonlinear dynamical system and a bilinear representation for a nonlinear control system. The problem of feedback stabilization of a nonlinear control system is then transformed to the stabilization of a bilinear control system. We propose a control Lyapunov function (CLF)-based approach for the design of stabilizing feedback controllers for the bilinear system. ","authors_text":"Bowen Huang, Umesh Vaidya, Xu Ma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-09-28T21:40:43Z","title":"Feedback Stabilization Using Koopman Operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00089","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3d94748a0942d85128b4ad9d78bc3ace1a2ad2d1321fdc8166c149eee7820437","target":"record","created_at":"2026-05-18T00:04:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"95ef2013b73c0ab9ab5738aad7ad7eb3e5e4e5f8d3d77ffd846e3c688e2c004a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-09-28T21:40:43Z","title_canon_sha256":"2616da76fe32be906911aafc079a483f841aa9c1251c8eb2ed79aeb9eb210751"},"schema_version":"1.0","source":{"id":"1810.00089","kind":"arxiv","version":1}},"canonical_sha256":"ace88cd80a7249848dc64369abb13fa9a48886091f09e8b2b8b5d0468a43b416","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ace88cd80a7249848dc64369abb13fa9a48886091f09e8b2b8b5d0468a43b416","first_computed_at":"2026-05-18T00:04:28.842352Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:28.842352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4g1eMl1e5nU1QytOAVu2A9IefvTyaRT500xXR7HrgXhr+UpoW/BrA2Ky3uHAuZk/7aIAxgeT72iPAp1Kok6AAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:28.842983Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.00089","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d94748a0942d85128b4ad9d78bc3ace1a2ad2d1321fdc8166c149eee7820437","sha256:65f4244f24e97ad1596bcde28cd95a3f55e82e93ab9d91c891aff8c9591132ed"],"state_sha256":"4acaaa91d589bbea53685746ab22112f6b8c934d5388e030af09774cfc7b8fa6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IKXDa9XXcp5vJq53YfQCXSFwo4DUjbN1qNaQ7iCi0rRaLwczxRFRsaLOVstGPookaqfv64AmHChewDy+YjWTBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T00:57:31.095177Z","bundle_sha256":"3d40d4bddfdffbdc27e0eeddd679388fdc32703c8d6b6517acf36b6973d6aa64"}}