{"id":"https://openalex.org/W3145829828","doi":"https://doi.org/10.1109/cdc45484.2021.9682955","title":"On the Stability of Nonlinear Receding Horizon Control: A Geometric Perspective","display_name":"On the Stability of Nonlinear Receding Horizon Control: A Geometric Perspective","publication_year":2021,"publication_date":"2021-12-14","ids":{"openalex":"https://openalex.org/W3145829828","doi":"https://doi.org/10.1109/cdc45484.2021.9682955","mag":"3145829828"},"language":"en","primary_location":{"id":"doi:10.1109/cdc45484.2021.9682955","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc45484.2021.9682955","pdf_url":null,"source":{"id":"https://openalex.org/S4363607724","display_name":"2021 60th IEEE Conference on Decision and Control (CDC)","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":"2021 60th IEEE Conference on Decision and Control (CDC)","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/A5085796854","display_name":"Tyler Westenbroek","orcid":"https://orcid.org/0000-0003-1111-3118"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Tyler Westenbroek","raw_affiliation_strings":["University of California at Berkeley,Department of Electrical Engineering and Computer Sciences,USA"],"affiliations":[{"raw_affiliation_string":"University of California at Berkeley,Department of Electrical Engineering and Computer Sciences,USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037154191","display_name":"Max Simchowitz","orcid":"https://orcid.org/0000-0001-9900-1238"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Max Simchowitz","raw_affiliation_strings":["University of California at Berkeley,Department of Electrical Engineering and Computer Sciences,USA"],"affiliations":[{"raw_affiliation_string":"University of California at Berkeley,Department of Electrical Engineering and Computer Sciences,USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049812527","display_name":"Michael I. Jordan","orcid":"https://orcid.org/0000-0001-8935-817X"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael I. Jordan","raw_affiliation_strings":["University of California at Berkeley,Department of Electrical Engineering and Computer Sciences,USA"],"affiliations":[{"raw_affiliation_string":"University of California at Berkeley,Department of Electrical Engineering and Computer Sciences,USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103101043","display_name":"S. Shankar Sastry","orcid":null},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S. Shankar Sastry","raw_affiliation_strings":["University of California at Berkeley,Department of Electrical Engineering and Computer Sciences,USA"],"affiliations":[{"raw_affiliation_string":"University of California at Berkeley,Department of Electrical Engineering and Computer Sciences,USA","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5085796854"],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":1.3191,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.74068813,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"742","last_page":"749"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9998999834060669,"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":0.9998999834060669,"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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9987000226974487,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9941999912261963,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6447733044624329},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.6447674036026001},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5903680324554443},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5703502893447876},{"id":"https://openalex.org/keywords/horizon","display_name":"Horizon","score":0.5315492153167725},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5067687630653381},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4923015832901001},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4852016270160675},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4599337875843048},{"id":"https://openalex.org/keywords/implementation","display_name":"Implementation","score":0.4517036974430084},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.44345709681510925},{"id":"https://openalex.org/keywords/perspective","display_name":"Perspective (graphical)","score":0.42515718936920166},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.417265921831131},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.4139879047870636},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3829019069671631},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.10622107982635498}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6447733044624329},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.6447674036026001},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5903680324554443},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5703502893447876},{"id":"https://openalex.org/C159176650","wikidata":"https://www.wikidata.org/wiki/Q43261","display_name":"Horizon","level":2,"score":0.5315492153167725},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5067687630653381},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4923015832901001},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4852016270160675},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4599337875843048},{"id":"https://openalex.org/C26713055","wikidata":"https://www.wikidata.org/wiki/Q245962","display_name":"Implementation","level":2,"score":0.4517036974430084},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.44345709681510925},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.42515718936920166},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.417265921831131},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.4139879047870636},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3829019069671631},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.10622107982635498},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc45484.2021.9682955","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc45484.2021.9682955","pdf_url":null,"source":{"id":"https://openalex.org/S4363607724","display_name":"2021 60th IEEE Conference on Decision and Control (CDC)","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":"2021 60th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","score":0.5699999928474426,"id":"https://metadata.un.org/sdg/9"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1537335979","https://openalex.org/W1548148540","https://openalex.org/W1561445488","https://openalex.org/W1578936488","https://openalex.org/W1978956894","https://openalex.org/W1988505764","https://openalex.org/W2016211524","https://openalex.org/W2041076275","https://openalex.org/W2048922416","https://openalex.org/W2097467365","https://openalex.org/W2102737570","https://openalex.org/W2110703708","https://openalex.org/W2119925384","https://openalex.org/W2122136962","https://openalex.org/W2128818348","https://openalex.org/W2142493442","https://openalex.org/W2170344654","https://openalex.org/W2182977695","https://openalex.org/W2341171179","https://openalex.org/W2396019715","https://openalex.org/W2474090883","https://openalex.org/W2519585338","https://openalex.org/W2521454744","https://openalex.org/W2798766386","https://openalex.org/W2886474253","https://openalex.org/W2892999459","https://openalex.org/W2894604724","https://openalex.org/W2946431541","https://openalex.org/W2963092340","https://openalex.org/W2964031251","https://openalex.org/W2964106499","https://openalex.org/W3145829828","https://openalex.org/W4237591687","https://openalex.org/W4249919931","https://openalex.org/W4250739957","https://openalex.org/W6727033717"],"related_works":["https://openalex.org/W2120447654","https://openalex.org/W2977179488","https://openalex.org/W2144453115","https://openalex.org/W2128223750","https://openalex.org/W4238532390","https://openalex.org/W2188872161","https://openalex.org/W2002978035","https://openalex.org/W797688974","https://openalex.org/W2209382646","https://openalex.org/W2282793296"],"abstract_inverted_index":{"The":[0],"widespread":[1],"adoption":[2],"of":[3,19,64,106,150,160,172,178],"nonlinear":[4,77],"Receding":[5],"Horizon":[6],"Control":[7],"(RHC)":[8],"strategies":[9],"by":[10],"industry":[11],"has":[12],"led":[13],"to":[14,23,44,86,99,122,136,168],"more":[15],"than":[16],"30":[17],"years":[18],"intense":[20],"research":[21],"efforts":[22],"provide":[24],"stability":[25,74],"guarantees":[26,33,75],"for":[27,53,76],"these":[28],"methods.":[29],"However,":[30],"current":[31],"theoretical":[32],"require":[34],"that":[35,132],"each":[36],"(generally":[37],"nonconvex)":[38],"planning":[39,82,138],"problem":[40,83],"can":[41],"be":[42],"solved":[43,85],"(approximate)":[45],"global":[46,93,148,173],"optimality,":[47],"which":[48],"is":[49,84,97],"an":[50],"unrealistic":[51],"requirement":[52],"the":[54,69,80,137,147,151,158,166,170,176],"derivative-based":[55],"local":[56],"optimization":[57],"methods":[58],"generally":[59],"used":[60],"in":[61,141,175],"practical":[62],"implementations":[63],"RHC.":[65],"This":[66],"paper":[67],"takes":[68],"first":[70],"step":[71],"towards":[72],"understanding":[73],"RHC":[78,123],"when":[79],"inner":[81],"first-order":[87,120],"stationary":[88],"points,":[89],"but":[90],"not":[91],"necessarily":[92],"optima.":[94],"Special":[95],"attention":[96],"given":[98],"feedback":[100],"linearizable":[101,126],"systems,":[102],"and":[103,108,153],"a":[104,142,154],"mixture":[105],"positive":[107],"negative":[109],"results":[110,164],"are":[111,140],"provided.":[112],"We":[113],"establish":[114],"that,":[115],"under":[116],"certain":[117,143],"strong":[118],"conditions,":[119],"solutions":[121],"exponentially":[124],"stabilize":[125],"systems.":[127],"Crucially,":[128],"this":[129,161],"guarantee":[130],"requires":[131],"state":[133],"costs":[134],"applied":[135],"problems":[139],"sense":[144],"\u2018compatible\u2019":[145],"with":[146],"geometry":[149,174],"system,":[152],"simple":[155],"counter-example":[156],"demonstrates":[157],"necessity":[159],"condition.":[162],"These":[163],"highlight":[165],"need":[167],"rethink":[169],"role":[171],"context":[177],"optimization-based":[179],"control.":[180]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}