{"id":"https://openalex.org/W4294691995","doi":"https://doi.org/10.23919/acc53348.2022.9867685","title":"Equivalent Linear Programming Formulations for Robust Trajectory Planning Under Input Dependent Uncertainties","display_name":"Equivalent Linear Programming Formulations for Robust Trajectory Planning Under Input Dependent Uncertainties","publication_year":2022,"publication_date":"2022-06-08","ids":{"openalex":"https://openalex.org/W4294691995","doi":"https://doi.org/10.23919/acc53348.2022.9867685"},"language":"en","primary_location":{"id":"doi:10.23919/acc53348.2022.9867685","is_oa":false,"landing_page_url":"https://doi.org/10.23919/acc53348.2022.9867685","pdf_url":null,"source":{"id":"https://openalex.org/S4363607732","display_name":"2022 American Control Conference (ACC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 American Control Conference (ACC)","raw_type":"proceedings-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/A5064153605","display_name":"Oliver Sheridan","orcid":"https://orcid.org/0009-0005-5024-8914"},"institutions":[{"id":"https://openalex.org/I46020346","display_name":"American Institute of Aeronautics and Astronautics","ror":"https://ror.org/00a1rzv11","country_code":"US","type":"other","lineage":["https://openalex.org/I46020346"]},{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Oliver Sheridan","raw_affiliation_strings":["University of Washington,Department of Aeronautics &#x0026; Astronautics,Seattle,WA,USA,98195-2400"],"affiliations":[{"raw_affiliation_string":"University of Washington,Department of Aeronautics &#x0026; Astronautics,Seattle,WA,USA,98195-2400","institution_ids":["https://openalex.org/I46020346","https://openalex.org/I201448701"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044772884","display_name":"Beh\u00e7et A\u00e7\u0131kme\u015fe","orcid":"https://orcid.org/0000-0002-8693-8109"},"institutions":[{"id":"https://openalex.org/I46020346","display_name":"American Institute of Aeronautics and Astronautics","ror":"https://ror.org/00a1rzv11","country_code":"US","type":"other","lineage":["https://openalex.org/I46020346"]},{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Behcet Acikmese","raw_affiliation_strings":["University of Washington,Department of Aeronautics &#x0026; Astronautics,Seattle,WA,USA,98195-2400"],"affiliations":[{"raw_affiliation_string":"University of Washington,Department of Aeronautics &#x0026; Astronautics,Seattle,WA,USA,98195-2400","institution_ids":["https://openalex.org/I46020346","https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5064153605"],"corresponding_institution_ids":["https://openalex.org/I201448701","https://openalex.org/I46020346"],"apc_list":null,"apc_paid":null,"fwci":1.0617,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.72669363,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"1873","last_page":"1878"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9973999857902527,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9973999857902527,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9927999973297119,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9771000146865845,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6313044428825378},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5859361886978149},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5612709522247314},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.5268558263778687},{"id":"https://openalex.org/keywords/robust-optimization","display_name":"Robust optimization","score":0.5191404223442078},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.489391028881073},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.44994229078292847},{"id":"https://openalex.org/keywords/linear-matrix-inequality","display_name":"Linear matrix inequality","score":0.44415128231048584},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.4388166666030884},{"id":"https://openalex.org/keywords/robust-control","display_name":"Robust control","score":0.4384266138076782},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.43788546323776245},{"id":"https://openalex.org/keywords/linear-inequality","display_name":"Linear inequality","score":0.43391096591949463},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.4237772822380066},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.41449886560440063},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.30413633584976196},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.23930561542510986}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6313044428825378},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5859361886978149},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5612709522247314},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.5268558263778687},{"id":"https://openalex.org/C193254401","wikidata":"https://www.wikidata.org/wiki/Q2160088","display_name":"Robust optimization","level":2,"score":0.5191404223442078},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.489391028881073},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.44994229078292847},{"id":"https://openalex.org/C201829737","wikidata":"https://www.wikidata.org/wiki/Q2022760","display_name":"Linear matrix inequality","level":2,"score":0.44415128231048584},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.4388166666030884},{"id":"https://openalex.org/C31531917","wikidata":"https://www.wikidata.org/wiki/Q915157","display_name":"Robust control","level":3,"score":0.4384266138076782},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.43788546323776245},{"id":"https://openalex.org/C84135550","wikidata":"https://www.wikidata.org/wiki/Q3154022","display_name":"Linear inequality","level":3,"score":0.43391096591949463},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.4237772822380066},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.41449886560440063},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.30413633584976196},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.23930561542510986},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"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/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.23919/acc53348.2022.9867685","is_oa":false,"landing_page_url":"https://doi.org/10.23919/acc53348.2022.9867685","pdf_url":null,"source":{"id":"https://openalex.org/S4363607732","display_name":"2022 American Control Conference (ACC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 American Control Conference (ACC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5199999809265137,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W134689491","https://openalex.org/W1581411521","https://openalex.org/W1602410440","https://openalex.org/W1880805667","https://openalex.org/W1982648044","https://openalex.org/W2006455928","https://openalex.org/W2047360753","https://openalex.org/W2057553555","https://openalex.org/W2063906864","https://openalex.org/W2080641008","https://openalex.org/W2097506640","https://openalex.org/W2125160645","https://openalex.org/W2131116400","https://openalex.org/W2161443056","https://openalex.org/W2171505650","https://openalex.org/W2474323855","https://openalex.org/W2513178932","https://openalex.org/W2601429851","https://openalex.org/W2809317103","https://openalex.org/W2909022610","https://openalex.org/W2972643957","https://openalex.org/W3102244603","https://openalex.org/W4210838762","https://openalex.org/W4250589301","https://openalex.org/W4251616545","https://openalex.org/W4297825594","https://openalex.org/W6605473481","https://openalex.org/W6634802212","https://openalex.org/W6636177105","https://openalex.org/W6682856452","https://openalex.org/W6696497002","https://openalex.org/W6721173772","https://openalex.org/W6735476400"],"related_works":["https://openalex.org/W2165589608","https://openalex.org/W3006682748","https://openalex.org/W3093557575","https://openalex.org/W2354231916","https://openalex.org/W3182767856","https://openalex.org/W2162140574","https://openalex.org/W1097487277","https://openalex.org/W2354073393","https://openalex.org/W2361009070","https://openalex.org/W4206501120"],"abstract_inverted_index":{"We":[0,48,186],"consider":[1,22],"the":[2,17,25,36,69,79,84,112,132,147,153,157,177],"problem":[3,72,116,121,149,184],"of":[4,27,107,146,152],"optimal":[5],"trajectory":[6,71,114],"planning":[7,115],"for":[8],"discrete-time":[9],"linear":[10,52,65,139,179],"dynamical":[11],"systems":[12,58],"with":[13,30,122],"bounded":[14],"uncertainty":[15,23,81],"in":[16,24,44,156],"inputs.":[18],"In":[19],"particular,":[20],"we":[21,102,129],"form":[26],"control":[28,38],"disturbance":[29,41],"bounds":[31],"that":[32,42,50,91,131],"are":[33,87,165],"proportional":[34],"to":[35,96,110,172],"nominal":[37],"and":[39],"exogenous":[40],"lies":[43],"a":[45,118,143,195],"known":[46],"polytope.":[47],"show":[49],"robust":[51,70,113],"inequality":[53,66],"state":[54],"constraints":[55,125,134],"on":[56,194],"such":[57],"can":[59,73,92,135],"be":[60,74,93,136],"equivalently":[61],"reformulated":[62],"as":[63,117],"deterministic":[64,119,178],"constraints,":[67],"hence":[68],"solved":[75,94],"without":[76],"conservatism":[77],"within":[78],"specified":[80],"bounds.":[82],"Furthermore,":[83],"resulting":[85],"problems":[86,90],"convex":[88,108],"optimization":[89,109,120,148],"efficiently":[95],"global":[97],"optimality.":[98],"To":[99],"this":[100],"end,":[101],"first":[103],"utilize":[104],"duality":[105],"theory":[106],"formulate":[111],"some":[123],"bilinear":[124,133,158],"(Lemma":[126,160],"(1)).":[127],"Then":[128],"observe":[130],"replaced":[137],"by":[138,141],"ones":[140],"finding":[142],"closed-form":[144],"solution":[145],"over":[150],"one":[151],"two":[154,163],"variables":[155],"terms":[159],"(2)).":[161],"These":[162],"lemmas":[164],"our":[166,183,189],"main":[167],"contributions,":[168],"which":[169,175,181],"together":[170],"lead":[171],"Theorem":[173],"(1),":[174],"allows":[176],"reformulation":[180],"renders":[182],"tractable.":[185],"then":[187],"demonstrate":[188],"method":[190],"via":[191],"numerical":[192],"simulations":[193],"simple":[196],"example":[197],"problem.":[198]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
