{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:CLYGM2VFJ32ZF2RHQM2UBO5QHU","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":"6022386c4647c8568dcfa425f3f8cdb261fd5b03b702162350107d188a5e01b5","cross_cats_sorted":["cs.SY","eess.SY","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-09-25T22:27:38Z","title_canon_sha256":"cc3a26ec0ed747d23cd99b5a1dbcc5722372320f33e909bf746f619785d7bdf5"},"schema_version":"1.0","source":{"id":"1909.11798","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.11798","created_at":"2026-07-05T00:07:37Z"},{"alias_kind":"arxiv_version","alias_value":"1909.11798v2","created_at":"2026-07-05T00:07:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.11798","created_at":"2026-07-05T00:07:37Z"},{"alias_kind":"pith_short_12","alias_value":"CLYGM2VFJ32Z","created_at":"2026-07-05T00:07:37Z"},{"alias_kind":"pith_short_16","alias_value":"CLYGM2VFJ32ZF2RH","created_at":"2026-07-05T00:07:37Z"},{"alias_kind":"pith_short_8","alias_value":"CLYGM2VF","created_at":"2026-07-05T00:07:37Z"}],"graph_snapshots":[{"event_id":"sha256:4131cd4dfbecdee5e2f53f23c74d2357196c371edb36a640ea3935fb605c70a4","target":"graph","created_at":"2026-07-05T00:07:37Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1909.11798/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper considers the synthesis of optimal safe controllers based on density functions. We present an algorithm for robust constrained optimal control synthesis using the duality relationship between the density function and the value function. The density function follows the Liouville equation and is the dual of the value function, which satisfies Bellman's optimality principle. Thanks to density functions, constraints over the distribution of states, such as safety constraints, can be posed straightforwardly in an optimal control problem. The constrained optimal control problem is then s","authors_text":"Aaron D. Ames, Mohamadreza Ahmadi, Yuxiao Chen","cross_cats":["cs.SY","eess.SY","math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-09-25T22:27:38Z","title":"Optimal Safe Controller Synthesis: A Density Function Approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.11798","kind":"arxiv","version":2},"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":"sha256:48e25a3c8adef5d87154afa1779ab6987417917af07ab403e3e697af074f330e","target":"record","created_at":"2026-07-05T00:07:37Z","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":"6022386c4647c8568dcfa425f3f8cdb261fd5b03b702162350107d188a5e01b5","cross_cats_sorted":["cs.SY","eess.SY","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-09-25T22:27:38Z","title_canon_sha256":"cc3a26ec0ed747d23cd99b5a1dbcc5722372320f33e909bf746f619785d7bdf5"},"schema_version":"1.0","source":{"id":"1909.11798","kind":"arxiv","version":2}},"canonical_sha256":"12f0666aa54ef592ea27833540bbb03d2a7e3ea70f4057ff3ccf5a869598f322","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12f0666aa54ef592ea27833540bbb03d2a7e3ea70f4057ff3ccf5a869598f322","first_computed_at":"2026-07-05T00:07:37.998703Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:07:37.998703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c7jbGTVTojHcYqhIM5S3fD/IKWY+KMUKBIHD9EhD+kH/7QMBDUuY4rdiujIgfHLbs4sOeAqlp128QpF1rvNBBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:07:37.999115Z","signed_message":"canonical_sha256_bytes"},"source_id":"1909.11798","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48e25a3c8adef5d87154afa1779ab6987417917af07ab403e3e697af074f330e","sha256:4131cd4dfbecdee5e2f53f23c74d2357196c371edb36a640ea3935fb605c70a4"],"state_sha256":"9d6a0aa0241a53d0740f855a2f74307b41a56939a5fd7525320f3edd57006ec3"}