{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:XOS25AFK22B5WTTHVDTTPLL2FS","short_pith_number":"pith:XOS25AFK","schema_version":"1.0","canonical_sha256":"bba5ae80aad683db4e67a8e737ad7a2c8804fb1cb7e417142004bf4f83ae48c7","source":{"kind":"arxiv","id":"2607.04006","version":1},"attestation_state":"computed","paper":{"title":"Finite-Sample Closed-Loop Stability of Model Predictive Path Integral Control for Linear Time-Invariant Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.RO","cs.SY","eess.SY"],"primary_cat":"math.OC","authors_text":"Hunmin Kim, Hyung-Jin Yoon","submitted_at":"2026-07-04T20:02:17Z","abstract_excerpt":"We establish finite-sample closed-loop stability guarantees for Model Predictive Path Integral (MPPI) control applied to discrete-time Linear Time-Invariant (LTI) systems with additive Gaussian process disturbances. The key observation is that, for unconstrained LTI/quadratic systems with the DARE terminal cost, the exact finite-horizon MPC law has the same first control action as the infinite-horizon LQR law for every planning horizon. Thus, finite-sample MPPI can be analyzed as a stochastic perturbation of LQR. First, we show that the MPPI control law approximates the LQR feedback with high "},"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":"2607.04006","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-04T20:02:17Z","cross_cats_sorted":["cs.RO","cs.SY","eess.SY"],"title_canon_sha256":"75a587d27fa7af493a107fb4cfd180965a45e769113178f26f056d496bdaeb4f","abstract_canon_sha256":"795cfdd9d451c844ce0a46b7799d3531548ebdead530d17709a3a36a0279b3f6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T02:18:52.756162Z","signature_b64":"lo3spOQ+Za06ZfjqtmTrzr1jkU0yJHXjftDrl0vu4tHKQ0zpQ6S4A9JTbTpNAA0tppnNXJvUsJxhEBo2cHN+Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bba5ae80aad683db4e67a8e737ad7a2c8804fb1cb7e417142004bf4f83ae48c7","last_reissued_at":"2026-07-07T02:18:52.755554Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T02:18:52.755554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite-Sample Closed-Loop Stability of Model Predictive Path Integral Control for Linear Time-Invariant Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.RO","cs.SY","eess.SY"],"primary_cat":"math.OC","authors_text":"Hunmin Kim, Hyung-Jin Yoon","submitted_at":"2026-07-04T20:02:17Z","abstract_excerpt":"We establish finite-sample closed-loop stability guarantees for Model Predictive Path Integral (MPPI) control applied to discrete-time Linear Time-Invariant (LTI) systems with additive Gaussian process disturbances. The key observation is that, for unconstrained LTI/quadratic systems with the DARE terminal cost, the exact finite-horizon MPC law has the same first control action as the infinite-horizon LQR law for every planning horizon. Thus, finite-sample MPPI can be analyzed as a stochastic perturbation of LQR. First, we show that the MPPI control law approximates the LQR feedback with high "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.04006","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.04006/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.04006","created_at":"2026-07-07T02:18:52.755639+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.04006v1","created_at":"2026-07-07T02:18:52.755639+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.04006","created_at":"2026-07-07T02:18:52.755639+00:00"},{"alias_kind":"pith_short_12","alias_value":"XOS25AFK22B5","created_at":"2026-07-07T02:18:52.755639+00:00"},{"alias_kind":"pith_short_16","alias_value":"XOS25AFK22B5WTTH","created_at":"2026-07-07T02:18:52.755639+00:00"},{"alias_kind":"pith_short_8","alias_value":"XOS25AFK","created_at":"2026-07-07T02:18:52.755639+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.06945","citing_title":"Stochastic Stability of Nonlinear MPPI via Contraction Theory and Control Lyapunov Functions","ref_index":2,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XOS25AFK22B5WTTHVDTTPLL2FS","json":"https://pith.science/pith/XOS25AFK22B5WTTHVDTTPLL2FS.json","graph_json":"https://pith.science/api/pith-number/XOS25AFK22B5WTTHVDTTPLL2FS/graph.json","events_json":"https://pith.science/api/pith-number/XOS25AFK22B5WTTHVDTTPLL2FS/events.json","paper":"https://pith.science/paper/XOS25AFK"},"agent_actions":{"view_html":"https://pith.science/pith/XOS25AFK22B5WTTHVDTTPLL2FS","download_json":"https://pith.science/pith/XOS25AFK22B5WTTHVDTTPLL2FS.json","view_paper":"https://pith.science/paper/XOS25AFK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.04006&json=true","fetch_graph":"https://pith.science/api/pith-number/XOS25AFK22B5WTTHVDTTPLL2FS/graph.json","fetch_events":"https://pith.science/api/pith-number/XOS25AFK22B5WTTHVDTTPLL2FS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XOS25AFK22B5WTTHVDTTPLL2FS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XOS25AFK22B5WTTHVDTTPLL2FS/action/storage_attestation","attest_author":"https://pith.science/pith/XOS25AFK22B5WTTHVDTTPLL2FS/action/author_attestation","sign_citation":"https://pith.science/pith/XOS25AFK22B5WTTHVDTTPLL2FS/action/citation_signature","submit_replication":"https://pith.science/pith/XOS25AFK22B5WTTHVDTTPLL2FS/action/replication_record"}},"created_at":"2026-07-07T02:18:52.755639+00:00","updated_at":"2026-07-07T02:18:52.755639+00:00"}