{"id":"https://openalex.org/W4406012277","doi":"https://doi.org/10.1109/tac.2025.3525569","title":"Motion Planning for Parabolic Equations Using Flatness and Finite-Difference Approximations","display_name":"Motion Planning for Parabolic Equations Using Flatness and Finite-Difference Approximations","publication_year":2025,"publication_date":"2025-01-02","ids":{"openalex":"https://openalex.org/W4406012277","doi":"https://doi.org/10.1109/tac.2025.3525569"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2025.3525569","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2025.3525569","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001688604","display_name":"Soham Chatterjee","orcid":"https://orcid.org/0000-0003-0814-8424"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Soham Chatterjee","raw_affiliation_strings":["Centre for Systems and Control, Indian Institute of Technology Bombay, Mumbai, India"],"raw_orcid":"https://orcid.org/0000-0003-0814-8424","affiliations":[{"raw_affiliation_string":"Centre for Systems and Control, Indian Institute of Technology Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083858098","display_name":"Vivek Natarajan","orcid":"https://orcid.org/0000-0001-6757-6176"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Vivek Natarajan","raw_affiliation_strings":["Centre for Systems and Control, Indian Institute of Technology Bombay, Mumbai, India"],"raw_orcid":"https://orcid.org/0000-0001-6757-6176","affiliations":[{"raw_affiliation_string":"Centre for Systems and Control, Indian Institute of Technology Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I162827531"],"apc_list":null,"apc_paid":null,"fwci":2.3336,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.86350388,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"70","issue":"7","first_page":"4439","last_page":"4454"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9761000275611877,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9491999745368958,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.765082597732544},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.7281463146209717},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6177887320518494},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5908291935920715},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.5814367532730103},{"id":"https://openalex.org/keywords/flatness","display_name":"Flatness (cosmology)","score":0.5395320057868958},{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.5269019603729248},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5004043579101562},{"id":"https://openalex.org/keywords/heat-equation","display_name":"Heat equation","score":0.4802396893501282},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.300022691488266},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08425506949424744}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.765082597732544},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.7281463146209717},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6177887320518494},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5908291935920715},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.5814367532730103},{"id":"https://openalex.org/C2778530986","wikidata":"https://www.wikidata.org/wiki/Q5457948","display_name":"Flatness (cosmology)","level":3,"score":0.5395320057868958},{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.5269019603729248},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5004043579101562},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.4802396893501282},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.300022691488266},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08425506949424744},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C26405456","wikidata":"https://www.wikidata.org/wiki/Q338","display_name":"Cosmology","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2025.3525569","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2025.3525569","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.6299999952316284,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W603018635","https://openalex.org/W1527296550","https://openalex.org/W1568807173","https://openalex.org/W1618634548","https://openalex.org/W1877697960","https://openalex.org/W1966686724","https://openalex.org/W1988889896","https://openalex.org/W2001950147","https://openalex.org/W2017682049","https://openalex.org/W2030571205","https://openalex.org/W2030634628","https://openalex.org/W2045512695","https://openalex.org/W2064765091","https://openalex.org/W2065297540","https://openalex.org/W2082009002","https://openalex.org/W2104412804","https://openalex.org/W2117623527","https://openalex.org/W2126805081","https://openalex.org/W2135669655","https://openalex.org/W2139614938","https://openalex.org/W2167532635","https://openalex.org/W2570676862","https://openalex.org/W2592178514","https://openalex.org/W2897812427","https://openalex.org/W3111685920","https://openalex.org/W3119794235","https://openalex.org/W4301386114"],"related_works":["https://openalex.org/W2755654899","https://openalex.org/W2114304162","https://openalex.org/W3215273227","https://openalex.org/W2316191048","https://openalex.org/W3037143972","https://openalex.org/W3185750406","https://openalex.org/W2112628619","https://openalex.org/W2259168425","https://openalex.org/W4389471227","https://openalex.org/W2979903828"],"abstract_inverted_index":{"We":[0,51,105,188],"consider":[1],"the":[2,42,60,64,68,80,96,102,109,128,132,151,158,180,198,223],"problem":[3,56],"of":[4,101,160,201],"finding":[5],"an":[6,85],"input":[7,86,117,123,176,220],"signal":[8,87,118,124,221],"which":[9,125,178],"transfers":[10,89],"a":[11,24,29,47,73,121,194,212,217],"linear":[12,74,203],"boundary":[13],"controlled":[14],"1D":[15,202],"parabolic":[16,65,103,133,147,164,181,204],"partial":[17],"differential":[18],"equation":[19,66,182],"with":[20,166],"spatially-varying":[21,168],"coefficients":[22,208],"from":[23,183],"given":[25,48],"initial":[26,34,97,224],"state":[27,225],"to":[28,71,114,120,144,154,186],"desired":[30,129],"final":[31,36,99],"state.":[32],"The":[33],"and":[35,41,98,156,209],"states":[37,93,100],"have":[38,138],"certain":[39],"smoothness":[40],"transfer":[43,130,179],"must":[44],"occur":[45],"over":[46],"time":[49],"interval.":[50],"address":[52],"this":[53,90,116,140,149,161,171,191],"motion":[54,141],"planning":[55,142],"by":[57,95],"first":[58,152],"discretizing":[59],"spatial":[61],"derivatives":[62],"in":[63,76],"using":[67,79],"finite-difference":[69],"approximation":[70],"obtain":[72],"ODE":[75,91],"time.":[77],"Then":[78],"flatness":[81],"approach":[82,143,162,172,192],"we":[83,173],"construct":[84,175],"that":[88,190],"between":[92],"determined":[94],"equation.":[104,134],"prove":[106],"that,":[107],"as":[108],"discretization":[110],"step":[111],"size":[112],"converges":[113,119],"zero,":[115],"limiting":[122],"can":[126,174],"perform":[127],"for":[131,163,197,215],"While":[135],"earlier":[136],"works":[137],"applied":[139],"constant":[145],"coefficient":[146],"equations,":[148],"is":[150,226],"work":[153],"investigate":[155],"establish":[157],"efficacy":[159],"equations":[165,205],"discontinuous":[167,207],"coefficients.":[169],"Using":[170],"signals":[177],"one":[184],"steady-state":[185],"another.":[187],"show":[189],"yields":[193],"new":[195],"proof":[196],"null":[199,218],"controllability":[200],"containing":[206],"also":[210],"present":[211],"numerical":[213],"scheme":[214],"constructing":[216],"control":[219],"when":[222],"piecewise":[227],"continuous.":[228]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
