{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:7Z5PIOW44PYVADFG354Q4BBNYN","short_pith_number":"pith:7Z5PIOW4","schema_version":"1.0","canonical_sha256":"fe7af43adce3f1500ca6df790e042dc348c5259be776a655237fb88c93bb8297","source":{"kind":"arxiv","id":"1810.01368","version":1},"attestation_state":"computed","paper":{"title":"Speed-Gradient Control of the Brockett Integrator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"A.L. Fradkov, M.V. Dolgopolik","submitted_at":"2018-10-02T16:57:03Z","abstract_excerpt":"A nonsmooth extension of the speed-gradient algorithms in finite form is proposed. The conditions ensuring control goal (convergence of the goal function to zero) are established. A new algorithm is applied to almost global stabilization of the Brockett integrator that has become a popular benchmark for nonsmooth and discontinuous algorithms. It is proved that the designed control law stabilizes the Brockett integrator for any initial point that does not lie on the x3-axis. Besides, it is shown that the speed-gradient algorithm ensures stabilization with an arbitrarily small control level. An "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1810.01368","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-10-02T16:57:03Z","cross_cats_sorted":[],"title_canon_sha256":"5b7f12481de73061626d9e323609b676aa93fe1022e26e7ab7af151a81eb2e9a","abstract_canon_sha256":"46004b7990deeba2b90464290b8e0173476eed9b65ea58a09dd37e7c3f382f44"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:18.140261Z","signature_b64":"XvNQWgdNEgIlZO4tU7EF6FYJeVPzj7XWIO6s+mH0JUOcaU2xUzhssvwEqf47hf5BaUbGDrHfKM0/9+DoU3fpCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe7af43adce3f1500ca6df790e042dc348c5259be776a655237fb88c93bb8297","last_reissued_at":"2026-05-18T00:04:18.139547Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:18.139547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Speed-Gradient Control of the Brockett Integrator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"A.L. Fradkov, M.V. Dolgopolik","submitted_at":"2018-10-02T16:57:03Z","abstract_excerpt":"A nonsmooth extension of the speed-gradient algorithms in finite form is proposed. The conditions ensuring control goal (convergence of the goal function to zero) are established. A new algorithm is applied to almost global stabilization of the Brockett integrator that has become a popular benchmark for nonsmooth and discontinuous algorithms. It is proved that the designed control law stabilizes the Brockett integrator for any initial point that does not lie on the x3-axis. Besides, it is shown that the speed-gradient algorithm ensures stabilization with an arbitrarily small control level. An "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01368","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1810.01368","created_at":"2026-05-18T00:04:18.139674+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.01368v1","created_at":"2026-05-18T00:04:18.139674+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.01368","created_at":"2026-05-18T00:04:18.139674+00:00"},{"alias_kind":"pith_short_12","alias_value":"7Z5PIOW44PYV","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_16","alias_value":"7Z5PIOW44PYVADFG","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_8","alias_value":"7Z5PIOW4","created_at":"2026-05-18T12:32:13.499390+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7Z5PIOW44PYVADFG354Q4BBNYN","json":"https://pith.science/pith/7Z5PIOW44PYVADFG354Q4BBNYN.json","graph_json":"https://pith.science/api/pith-number/7Z5PIOW44PYVADFG354Q4BBNYN/graph.json","events_json":"https://pith.science/api/pith-number/7Z5PIOW44PYVADFG354Q4BBNYN/events.json","paper":"https://pith.science/paper/7Z5PIOW4"},"agent_actions":{"view_html":"https://pith.science/pith/7Z5PIOW44PYVADFG354Q4BBNYN","download_json":"https://pith.science/pith/7Z5PIOW44PYVADFG354Q4BBNYN.json","view_paper":"https://pith.science/paper/7Z5PIOW4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.01368&json=true","fetch_graph":"https://pith.science/api/pith-number/7Z5PIOW44PYVADFG354Q4BBNYN/graph.json","fetch_events":"https://pith.science/api/pith-number/7Z5PIOW44PYVADFG354Q4BBNYN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7Z5PIOW44PYVADFG354Q4BBNYN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7Z5PIOW44PYVADFG354Q4BBNYN/action/storage_attestation","attest_author":"https://pith.science/pith/7Z5PIOW44PYVADFG354Q4BBNYN/action/author_attestation","sign_citation":"https://pith.science/pith/7Z5PIOW44PYVADFG354Q4BBNYN/action/citation_signature","submit_replication":"https://pith.science/pith/7Z5PIOW44PYVADFG354Q4BBNYN/action/replication_record"}},"created_at":"2026-05-18T00:04:18.139674+00:00","updated_at":"2026-05-18T00:04:18.139674+00:00"}