{"id":"https://openalex.org/W7155449860","doi":"https://doi.org/10.48550/arxiv.2604.20208","title":"Stochastic Barrier Certificates in the Presence of Dynamic Obstacles","display_name":"Stochastic Barrier Certificates in the Presence of Dynamic Obstacles","publication_year":2026,"publication_date":"2026-04-22","ids":{"openalex":"https://openalex.org/W7155449860","doi":"https://doi.org/10.48550/arxiv.2604.20208"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.20208","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.20208","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.20208","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058201964","display_name":"Rayan Mazouz","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mazouz, Rayan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134444003","display_name":"Luca Laurenti","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Laurenti, Luca","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5134390372","display_name":"Morteza Lahijanian","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lahijanian, Morteza","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.19949999451637268,"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"}},"topics":[{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.19949999451637268,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.1501999944448471,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.0778999999165535,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/obstacle","display_name":"Obstacle","score":0.5631999969482422},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5594000220298767},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.4690999984741211},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4154999852180481},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3991999924182892},{"id":"https://openalex.org/keywords/overhead","display_name":"Overhead (engineering)","score":0.39890000224113464},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3621000051498413}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5823000073432922},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.565500020980835},{"id":"https://openalex.org/C2776650193","wikidata":"https://www.wikidata.org/wiki/Q264661","display_name":"Obstacle","level":2,"score":0.5631999969482422},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5594000220298767},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.4690999984741211},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4154999852180481},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3991999924182892},{"id":"https://openalex.org/C2779960059","wikidata":"https://www.wikidata.org/wiki/Q7113681","display_name":"Overhead (engineering)","level":2,"score":0.39890000224113464},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3621000051498413},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.32829999923706055},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.2973000109195709},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.28780001401901245},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.27889999747276306},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.27649998664855957},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C46304622","wikidata":"https://www.wikidata.org/wiki/Q374814","display_name":"Certification","level":2,"score":0.25040000677108765},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.2502000033855438}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.20208","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.20208","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.20208","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.20208","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Safety":[0],"of":[1,18,45],"stochastic":[2,19],"dynamic":[3,8,116],"systems":[4,33,114],"in":[5,12],"environments":[6],"with":[7,115],"obstacles":[9,117],"is":[10],"studied":[11],"this":[13],"paper":[14],"through":[15],"the":[16,43,72],"lens":[17],"barrier":[20,28,97],"functions.":[21],"We":[22],"introduce":[23],"both":[24],"time-invariant":[25],"and":[26,79,129],"time-varying":[27,60,73,96,120],"certificates":[29,56,89,121],"for":[30,59],"discrete-time,":[31],"continuous-space":[32],"subject":[34],"to":[35,90],"uncertainty,":[36],"which":[37],"provide":[38],"certified":[39],"lower":[40],"bounds":[41,83],"on":[42,112],"probability":[44],"remaining":[46],"within":[47],"a":[48,52,103],"safe":[49],"set":[50],"over":[51,131],"finite":[53],"horizon.":[54],"These":[55],"explicitly":[57],"account":[58],"unsafe":[61],"regions":[62],"induced":[63],"by":[64],"obstacle":[65],"dynamics.":[66],"By":[67,87],"leveraging":[68],"Bellman's":[69],"optimality":[70],"perspective,":[71],"formulation":[74],"directly":[75],"captures":[76],"temporal":[77],"structure":[78],"yields":[80],"less":[81],"conservative":[82],"than":[84],"state-of-the-art":[85,132],"approaches.":[86],"restricting":[88],"polynomial":[91],"functions,":[92],"we":[93],"show":[94,118],"that":[95,119],"synthesis":[98],"can":[99],"be":[100],"formulated":[101],"as":[102],"convex":[104],"sum-of-squares":[105],"program,":[106],"enabling":[107],"tractable":[108],"optimization.":[109],"Empirical":[110],"evaluations":[111],"nonlinear":[113],"consistently":[122],"achieve":[123],"tight":[124],"guarantees,":[125],"demonstrating":[126],"improved":[127],"accuracy":[128],"scalability":[130],"methods.":[133]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-04-24T00:00:00"}
