{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:5KPAB74USQFU2Q7BHJ2N66FWFM","short_pith_number":"pith:5KPAB74U","canonical_record":{"source":{"id":"1705.05506","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-16T02:42:38Z","cross_cats_sorted":[],"title_canon_sha256":"6aaddaf83843a08f37d3ed23cadbe3028f4bb925a612adafee75ef4024882a01","abstract_canon_sha256":"e3e8555d60a6392d2a8f297dc223ab41fde9f91df0e164234db926aece90a06b"},"schema_version":"1.0"},"canonical_sha256":"ea9e00ff94940b4d43e13a74df78b62b1d6e689702c8d4caf7d8174c5f10ce17","source":{"kind":"arxiv","id":"1705.05506","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05506","created_at":"2026-05-18T00:44:22Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05506v1","created_at":"2026-05-18T00:44:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05506","created_at":"2026-05-18T00:44:22Z"},{"alias_kind":"pith_short_12","alias_value":"5KPAB74USQFU","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5KPAB74USQFU2Q7B","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5KPAB74U","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:5KPAB74USQFU2Q7BHJ2N66FWFM","target":"record","payload":{"canonical_record":{"source":{"id":"1705.05506","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-16T02:42:38Z","cross_cats_sorted":[],"title_canon_sha256":"6aaddaf83843a08f37d3ed23cadbe3028f4bb925a612adafee75ef4024882a01","abstract_canon_sha256":"e3e8555d60a6392d2a8f297dc223ab41fde9f91df0e164234db926aece90a06b"},"schema_version":"1.0"},"canonical_sha256":"ea9e00ff94940b4d43e13a74df78b62b1d6e689702c8d4caf7d8174c5f10ce17","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:22.570512Z","signature_b64":"8JpuThvQdvc7IFikPvp2gCyy/AfMg9IqZ5WriQw65LXUvItILMLnyZeFDyFsJkLAN/EnHFuV63LzeubxkzebDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea9e00ff94940b4d43e13a74df78b62b1d6e689702c8d4caf7d8174c5f10ce17","last_reissued_at":"2026-05-18T00:44:22.570043Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:22.570043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.05506","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":"2026-05-18T00:44:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j5WmiwpHeuzWdFGtV/VnucCdGbF4/rSDhfr3RmIkNkfRkAmwzQErBRugg4eBEKUWJ38WG4WwnJGgclNtJeIPAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:08:19.008226Z"},"content_sha256":"434dbe26d79a6f7d226a4560c23a614f79ee29d916c9f573f097422109e0f810","schema_version":"1.0","event_id":"sha256:434dbe26d79a6f7d226a4560c23a614f79ee29d916c9f573f097422109e0f810"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:5KPAB74USQFU2Q7BHJ2N66FWFM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic trajectory optimization for mechanical systems with parametric uncertainties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Evangelos A. Theodorou, George I. Boutselis, Gerardo De La Tore, Yunpeng Pan","submitted_at":"2017-05-16T02:42:38Z","abstract_excerpt":"In this paper we develop a novel, discrete-time optimal control framework for mechanical systems with uncertain model parameters. We consider finite-horizon problems where the performance index depends on the statistical moments of the stochastic system. Our approach constitutes an extension of the original Differential Dynamic Programming method and handles uncertainty through generalized Polynomial Chaos (gPC) theory. The developed iterative scheme is capable of controlling the probabilistic evolution of the dynamic system and can be used in planning and control. Moreover, its scalable and f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05506","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":"2026-05-18T00:44:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m5UYgmnNyD9rF7l0vLSSHUf2weuHvouKSW+kVm3mkUZHxvrCBbFpbVoFq1hxpJ13+LRxUgBPZfhJ2zqLTgD0CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:08:19.008955Z"},"content_sha256":"6168331dceb19c1992ef4b852673a5d63efa85cc8beac1a2f633c3c00d5f78e6","schema_version":"1.0","event_id":"sha256:6168331dceb19c1992ef4b852673a5d63efa85cc8beac1a2f633c3c00d5f78e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5KPAB74USQFU2Q7BHJ2N66FWFM/bundle.json","state_url":"https://pith.science/pith/5KPAB74USQFU2Q7BHJ2N66FWFM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5KPAB74USQFU2Q7BHJ2N66FWFM/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":"2026-05-30T08:08:19Z","links":{"resolver":"https://pith.science/pith/5KPAB74USQFU2Q7BHJ2N66FWFM","bundle":"https://pith.science/pith/5KPAB74USQFU2Q7BHJ2N66FWFM/bundle.json","state":"https://pith.science/pith/5KPAB74USQFU2Q7BHJ2N66FWFM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5KPAB74USQFU2Q7BHJ2N66FWFM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5KPAB74USQFU2Q7BHJ2N66FWFM","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":"e3e8555d60a6392d2a8f297dc223ab41fde9f91df0e164234db926aece90a06b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-16T02:42:38Z","title_canon_sha256":"6aaddaf83843a08f37d3ed23cadbe3028f4bb925a612adafee75ef4024882a01"},"schema_version":"1.0","source":{"id":"1705.05506","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05506","created_at":"2026-05-18T00:44:22Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05506v1","created_at":"2026-05-18T00:44:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05506","created_at":"2026-05-18T00:44:22Z"},{"alias_kind":"pith_short_12","alias_value":"5KPAB74USQFU","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5KPAB74USQFU2Q7B","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5KPAB74U","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:6168331dceb19c1992ef4b852673a5d63efa85cc8beac1a2f633c3c00d5f78e6","target":"graph","created_at":"2026-05-18T00:44:22Z","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 develop a novel, discrete-time optimal control framework for mechanical systems with uncertain model parameters. We consider finite-horizon problems where the performance index depends on the statistical moments of the stochastic system. Our approach constitutes an extension of the original Differential Dynamic Programming method and handles uncertainty through generalized Polynomial Chaos (gPC) theory. The developed iterative scheme is capable of controlling the probabilistic evolution of the dynamic system and can be used in planning and control. Moreover, its scalable and f","authors_text":"Evangelos A. Theodorou, George I. Boutselis, Gerardo De La Tore, Yunpeng Pan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-16T02:42:38Z","title":"Stochastic trajectory optimization for mechanical systems with parametric uncertainties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05506","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":"sha256:434dbe26d79a6f7d226a4560c23a614f79ee29d916c9f573f097422109e0f810","target":"record","created_at":"2026-05-18T00:44:22Z","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":"e3e8555d60a6392d2a8f297dc223ab41fde9f91df0e164234db926aece90a06b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-16T02:42:38Z","title_canon_sha256":"6aaddaf83843a08f37d3ed23cadbe3028f4bb925a612adafee75ef4024882a01"},"schema_version":"1.0","source":{"id":"1705.05506","kind":"arxiv","version":1}},"canonical_sha256":"ea9e00ff94940b4d43e13a74df78b62b1d6e689702c8d4caf7d8174c5f10ce17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea9e00ff94940b4d43e13a74df78b62b1d6e689702c8d4caf7d8174c5f10ce17","first_computed_at":"2026-05-18T00:44:22.570043Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:22.570043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8JpuThvQdvc7IFikPvp2gCyy/AfMg9IqZ5WriQw65LXUvItILMLnyZeFDyFsJkLAN/EnHFuV63LzeubxkzebDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:22.570512Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.05506","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:434dbe26d79a6f7d226a4560c23a614f79ee29d916c9f573f097422109e0f810","sha256:6168331dceb19c1992ef4b852673a5d63efa85cc8beac1a2f633c3c00d5f78e6"],"state_sha256":"9c98024012de2b0dfe412daa6ad37855888a79c28ca6f6a697edbfb8dcd2f2bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8qyTC/09yiTCcRxgQ6HuLC6JjAc3ukLSe4snTV11qmaIBMT2a8z+9c5x7koheC8bDwQBplDg4GjgW6p56XPnCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T08:08:19.012069Z","bundle_sha256":"017aa35a86fd17e3411e24aef111120615488cf1c7cf014ed6db0b1f9f0c391c"}}