{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:F5V24IVQ5RVW33E6Y4HHB74ECF","short_pith_number":"pith:F5V24IVQ","schema_version":"1.0","canonical_sha256":"2f6bae22b0ec6b6dec9ec70e70ff84114b7876f9307cecf46fafa19532c42355","source":{"kind":"arxiv","id":"1903.00988","version":2},"attestation_state":"computed","paper":{"title":"Optimal Control of Thermostatic Loads for Planning Aggregate Consumption: Characterization of Solution and Explicit Strategies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Abhishek Halder, Fernando A.C.C. Fontes, Jorge Becerril, P.R. Kumar","submitted_at":"2019-03-03T21:04:40Z","abstract_excerpt":"We consider the problem of planning the aggregate energy consumption for a set of thermostatically controlled loads for demand response, accounting price forecast trajectory and thermal comfort constraints. We address this as a continuous-time optimal control problem, and analytically characterize the structure of its solution in the general case. In the special case when the price forecast is monotone and the loads have equal dynamics, we show that it is possible to determine the solution in an explicit form. Taking this fact into account, we handle the non-monotone price case by considering "},"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":"1903.00988","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-03-03T21:04:40Z","cross_cats_sorted":[],"title_canon_sha256":"1cd35d397a50f6a8f4773843a010e846429882fa1575b486480325029c164be2","abstract_canon_sha256":"229d42db518013c6e836385a33811affe19730ce9249a1f8b650fb7dd97c3ae4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:45.687479Z","signature_b64":"5aXcGxQ0a8eHn7+Tx+cwoBgDNcXaXQ0BO6GRvf04krlFlX5V31AygxxUdm/vE74a4d2JJgG79b7RWBF4gWaiBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f6bae22b0ec6b6dec9ec70e70ff84114b7876f9307cecf46fafa19532c42355","last_reissued_at":"2026-05-17T23:46:45.687029Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:45.687029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal Control of Thermostatic Loads for Planning Aggregate Consumption: Characterization of Solution and Explicit Strategies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Abhishek Halder, Fernando A.C.C. Fontes, Jorge Becerril, P.R. Kumar","submitted_at":"2019-03-03T21:04:40Z","abstract_excerpt":"We consider the problem of planning the aggregate energy consumption for a set of thermostatically controlled loads for demand response, accounting price forecast trajectory and thermal comfort constraints. We address this as a continuous-time optimal control problem, and analytically characterize the structure of its solution in the general case. In the special case when the price forecast is monotone and the loads have equal dynamics, we show that it is possible to determine the solution in an explicit form. Taking this fact into account, we handle the non-monotone price case by considering "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00988","kind":"arxiv","version":2},"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":"1903.00988","created_at":"2026-05-17T23:46:45.687098+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.00988v2","created_at":"2026-05-17T23:46:45.687098+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.00988","created_at":"2026-05-17T23:46:45.687098+00:00"},{"alias_kind":"pith_short_12","alias_value":"F5V24IVQ5RVW","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"F5V24IVQ5RVW33E6","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"F5V24IVQ","created_at":"2026-05-18T12:33:15.570797+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/F5V24IVQ5RVW33E6Y4HHB74ECF","json":"https://pith.science/pith/F5V24IVQ5RVW33E6Y4HHB74ECF.json","graph_json":"https://pith.science/api/pith-number/F5V24IVQ5RVW33E6Y4HHB74ECF/graph.json","events_json":"https://pith.science/api/pith-number/F5V24IVQ5RVW33E6Y4HHB74ECF/events.json","paper":"https://pith.science/paper/F5V24IVQ"},"agent_actions":{"view_html":"https://pith.science/pith/F5V24IVQ5RVW33E6Y4HHB74ECF","download_json":"https://pith.science/pith/F5V24IVQ5RVW33E6Y4HHB74ECF.json","view_paper":"https://pith.science/paper/F5V24IVQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.00988&json=true","fetch_graph":"https://pith.science/api/pith-number/F5V24IVQ5RVW33E6Y4HHB74ECF/graph.json","fetch_events":"https://pith.science/api/pith-number/F5V24IVQ5RVW33E6Y4HHB74ECF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F5V24IVQ5RVW33E6Y4HHB74ECF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F5V24IVQ5RVW33E6Y4HHB74ECF/action/storage_attestation","attest_author":"https://pith.science/pith/F5V24IVQ5RVW33E6Y4HHB74ECF/action/author_attestation","sign_citation":"https://pith.science/pith/F5V24IVQ5RVW33E6Y4HHB74ECF/action/citation_signature","submit_replication":"https://pith.science/pith/F5V24IVQ5RVW33E6Y4HHB74ECF/action/replication_record"}},"created_at":"2026-05-17T23:46:45.687098+00:00","updated_at":"2026-05-17T23:46:45.687098+00:00"}