{"corpus_id":6939245,"paper_sha":"1f02648d45ff69d373099c038286ffd90bf92084","doi":"10.1109/TAC.2013.2250075","arxiv_id":"1111.1475","pmid":null,"pmcid":null,"mag_id":1996839950,"dblp_id":"journals/tac/BurgarthDHSY13","acl_id":null,"title":"Zero Forcing, Linear and Quantum Controllability for Systems Evolving on Networks","year":2011,"publication_date":"2011-11-07","venue":"IEEE Transactions on Automatic Control","journal":{"name":"IEEE Transactions on Automatic Control","pages":"2349-2354","volume":"58"},"journal_issn":null,"journal_title":null,"publication_types":["JournalArticle"],"pubmed_pub_types":null,"s2_fields_of_study":["Mathematics","Physics","Computer Science"],"reference_count":30,"citation_count":81,"influential_citation_count":3,"is_open_access":true,"arxiv_categories":["quant-ph","cond-mat.dis-nn","cond-mat.stat-mech","math.CO"],"arxiv_license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","arxiv_journal_ref":"IEEE Transactions on Automatic Control 58, 2349 (2013)","mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":"https://dr.lib.iastate.edu/bitstreams/14e06150-9c8a-48ce-9427-a66f8561a90b/download","s2_open_access_landing_url":"https://www.semanticscholar.org/paper/1f02648d45ff69d373099c038286ffd90bf92084","s2_open_access_license":null,"s2_open_access_status":"GREEN","pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"We study the dynamics of systems on networks from a linear algebraic perspective. The control theoretic concept of controllability describes the set of states that can be reached for these systems. Our main result says that controllability in the quantum sense, expressed by the Lie algebra rank condition, and controllability in the sense of linear systems, expressed by the controllability matrix rank condition, are equivalent conditions. We also investigate how the graph theoretic concept of a zero forcing set impacts the controllability property; if a set of vertices is a zero forcing set, the associated dynamical system is controllable. These results open up the possibility of further exploiting the analogy between networks, linear control systems theory, and quantum systems Lie algebraic theory. This study is motivated by several quantum systems currently under study, including continuous quantum walks modeling transport phenomena.","claims":[{"public_id":"cl_2ae7a129cbc735d10ce473fd2e263379","status":"active","text":"Controllability in the quantum sense, expressed by the Lie algebra rank condition, and controllability in the sense of linear systems, expressed by the controllability matrix rank condition, are equivalent conditions.","confidence":0.95,"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_2ae7a129cbc735d10ce473fd2e263379"},{"public_id":"cl_37caf13dd7ee6f0b1e565dbd16e55ea4","status":"active","text":"If a set of vertices is a zero forcing set, the associated dynamical system is controllable.","confidence":0.9,"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_37caf13dd7ee6f0b1e565dbd16e55ea4"}],"concepts":[{"public_id":"co_1a558c9fcf55fcdd8a05d92ff7344ff0","status":"active","name":"Lie algebra rank condition","description":"A condition for quantum controllability based on the rank of the associated Lie algebra.","types":["mathematical condition"],"aliases":[],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_1a558c9fcf55fcdd8a05d92ff7344ff0"},{"public_id":"co_50cd49c820479258470cc8999460f291","status":"active","name":"zero forcing set","description":"A set of vertices in a graph such that if initially colored, the entire graph becomes colored by a zero forcing process.","types":["graph theoretic concept"],"aliases":[],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_50cd49c820479258470cc8999460f291"},{"public_id":"co_60490982cbd74deee92aa665dc250037","status":"active","name":"controllability matrix rank condition","description":"A condition for linear systems controllability based on the rank of the controllability matrix.","types":["mathematical condition"],"aliases":[],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_60490982cbd74deee92aa665dc250037"},{"public_id":"co_767483026657dc26b6795b5d2ba999b8","status":"active","name":"networks","description":"Graph structures on which the systems evolve, studied from a linear algebraic perspective.","types":["mathematical structure"],"aliases":[],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_767483026657dc26b6795b5d2ba999b8"},{"public_id":"co_777695dbebc15690680ce5dcdd039466","status":"active","name":"dynamical system controllability","description":"The property that a dynamical system can be driven from any initial state to any target state.","types":["theoretical concept"],"aliases":[],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_777695dbebc15690680ce5dcdd039466"},{"public_id":"co_8dfcaf17ac20dfcf059e2c61592ea8d6","status":"active","name":"quantum controllability","description":"Controllability of a quantum system, expressed by the Lie algebra rank condition.","types":["theoretical concept"],"aliases":[],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_8dfcaf17ac20dfcf059e2c61592ea8d6"},{"public_id":"co_b031ca0f1e10e66fb21fe34e1c6b9c36","status":"active","name":"linear systems controllability","description":"Controllability of a linear dynamical system, expressed by the controllability matrix rank condition.","types":["theoretical concept"],"aliases":[],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_b031ca0f1e10e66fb21fe34e1c6b9c36"},{"public_id":"co_e9771b33906008c2649dfc82b17a6cab","status":"active","name":"continuous quantum walks","description":"Quantum systems modeling transport phenomena, motivating the study.","types":["quantum system"],"aliases":[],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_e9771b33906008c2649dfc82b17a6cab"}],"external_ids":{"DOI":"10.1109/TAC.2013.2250075","ArXiv":"1111.1475","PubMed":null,"PubMedCentral":null,"MAG":1996839950,"DBLP":"journals/tac/BurgarthDHSY13","ACL":null},"open_access":{"is_open_access":true,"pdf_url":"https://dr.lib.iastate.edu/bitstreams/14e06150-9c8a-48ce-9427-a66f8561a90b/download","landing_url":"https://www.semanticscholar.org/paper/1f02648d45ff69d373099c038286ffd90bf92084","source":"semantic_scholar","pdf_url_source":"semantic_scholar_open_access_pdf","license":null,"status":"GREEN","reason":null},"reference_availability":{"status":"available","references_indexed":true,"full_text_available":true,"full_text_source":"arxiv","count_basis":"semantic_scholar_metadata","extraction_status":"not_applicable","reason":null},"source":{"provider":"episteme2","base_corpus":"semantic_scholar_dump","freshness_mode":"unknown","basis":["semantic_scholar_metadata","postgres_metadata"],"limits":["paper metadata is based on indexed upstream scholarly datasets","claims and concepts are available only for extracted papers","absence of claims or concepts means no extracted graph data is available in this response"],"status":"available","degraded":false,"degraded_reasons":[],"diagnostics":{"status":"available","degraded":false,"degraded_reasons":[],"metadata_status":"available","graph_status":"available","abstract_status":"available"},"source_flags":1},"paper_id":635657,"paper_uid":"a2faf6c8-8fc8-40b6-9eaa-7ef8f7743585","canonical_identity":{"paper_id":635657,"paper_uid":"a2faf6c8-8fc8-40b6-9eaa-7ef8f7743585","identity_status":"available","lookup_basis":"semantic_scholar_external_id","compatibility_path":"corpus_id"},"url":"https://sah.borca.ai/papers/6939245"}