{"id":"https://openalex.org/W7163035185","doi":"https://doi.org/10.48550/arxiv.2605.30886","title":"Near-Optimal Mixed Strategy for Zero-Sum Linear-Quadratic Differential Games","display_name":"Near-Optimal Mixed Strategy for Zero-Sum Linear-Quadratic Differential Games","publication_year":2026,"publication_date":"2026-05-29","ids":{"openalex":"https://openalex.org/W7163035185","doi":"https://doi.org/10.48550/arxiv.2605.30886"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.30886","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.30886","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"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.2605.30886","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137589289","display_name":"Tao Xu","orcid":"https://orcid.org/0000-0003-1622-8985"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xu, Tao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137547139","display_name":"Wang Xi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xi, Wang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5004668792","display_name":"Jianping He","orcid":"https://orcid.org/0000-0002-6253-7802"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"He, Jianping","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/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.24770000576972961,"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/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.24770000576972961,"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/T14083","display_name":"Extremum Seeking Control Systems","score":0.1737000048160553,"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/T11031","display_name":"Game Theory and Applications","score":0.11729999631643295,"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/differential-game","display_name":"Differential game","score":0.7146999835968018},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5641000270843506},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.5031999945640564},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4819999933242798},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.48030000925064087},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.43160000443458557},{"id":"https://openalex.org/keywords/sequential-game","display_name":"Sequential game","score":0.4156999886035919},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4007999897003174},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.39239999651908875}],"concepts":[{"id":"https://openalex.org/C2779006483","wikidata":"https://www.wikidata.org/wiki/Q1973196","display_name":"Differential game","level":2,"score":0.7146999835968018},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5699999928474426},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5641000270843506},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.520799994468689},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.5031999945640564},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4819999933242798},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.48030000925064087},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.43160000443458557},{"id":"https://openalex.org/C73795354","wikidata":"https://www.wikidata.org/wiki/Q287618","display_name":"Sequential game","level":3,"score":0.4156999886035919},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4007999897003174},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.39239999651908875},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.38920000195503235},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3790000081062317},{"id":"https://openalex.org/C202556891","wikidata":"https://www.wikidata.org/wiki/Q1584646","display_name":"Repeated game","level":3,"score":0.37709999084472656},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.37459999322891235},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.3637000024318695},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3402000069618225},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.32690000534057617},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31850001215934753},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.3125999867916107},{"id":"https://openalex.org/C129537906","wikidata":"https://www.wikidata.org/wiki/Q7603913","display_name":"State variable","level":2,"score":0.29899999499320984},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.2978000044822693},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.29750001430511475},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.28780001401901245},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.28540000319480896},{"id":"https://openalex.org/C88959737","wikidata":"https://www.wikidata.org/wiki/Q1546627","display_name":"Strategy","level":3,"score":0.2849999964237213},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.2775000035762787},{"id":"https://openalex.org/C23130292","wikidata":"https://www.wikidata.org/wiki/Q5275358","display_name":"Differential privacy","level":2,"score":0.27129998803138733},{"id":"https://openalex.org/C2984679396","wikidata":"https://www.wikidata.org/wiki/Q7602986","display_name":"State dependent","level":2,"score":0.2531999945640564},{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.2517000138759613}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.30886","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.30886","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.30886","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.30886","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"score":0.49520936608314514,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Deriving":[0],"analytic":[1],"solutions":[2],"for":[3,26,86,114],"optimal":[4,83],"mixed":[5,24,51,131],"strategies":[6,25],"in":[7],"zero-sum":[8],"linear-quadratic":[9],"differential":[10,40],"games":[11],"(ZSLQDGs)":[12],"remains":[13],"an":[14,56],"open":[15],"problem.":[16],"In":[17],"this":[18],"paper,":[19],"we":[20,34,80,91,121,134],"analytically":[21,75],"synthesize":[22],"near-optimal":[23,130],"ZSLQDGs":[27],"and":[28,63,143,165],"establish":[29],"rigorous":[30],"performance":[31],"certifications.":[32],"Specifically,":[33],"construct":[35],"a":[36,100,109,123,156],"surrogate":[37,78,95],"pure-strategy":[38],"stochastic":[39],"game":[41,96,159],"(SDG)":[42],"by":[43,99,150],"matching":[44],"the":[45,50,69,77,87,94,129,138,144,161,167],"first":[46],"two":[47],"moments":[48],"of":[49,60],"strategies.":[52,132],"This":[53],"method":[54],"achieves":[55],"$\\mathcal{O}(\\bar\u03c0^2)$":[57],"weak":[58],"approximation":[59,141],"state":[61],"distributions":[62],"expected":[64],"costs":[65],"with":[66],"respect":[67],"to":[68,127],"maximum":[70],"commitment":[71],"delay":[72],"$\\bar\u03c0$.":[73],"By":[74],"resolving":[76],"SDG,":[79],"derive":[81],"closed-form":[82],"control":[84],"laws":[85],"matched":[88],"moments.":[89],"Crucially,":[90],"reveal":[92],"that":[93,136],"is":[97],"governed":[98],"Generalized":[101],"Riccati":[102],"Differential":[103],"Equation":[104],"(GRDE),":[105],"which":[106],"explicitly":[107],"dictates":[108],"dynamic":[110],"energy":[111],"allocation":[112],"law":[113],"variance":[115],"injection.":[116],"Building":[117],"on":[118,155],"these":[119],"solutions,":[120],"propose":[122],"robust":[124],"dual-routing":[125],"architecture":[126],"execute":[128],"Furthermore,":[133],"certify":[135],"both":[137],"global":[139],"value":[140],"error":[142],"strategy":[145],"suboptimality":[146],"gaps":[147],"are":[148],"bounded":[149],"$\\mathcal{O}(\\bar\u03c0^{\\frac{1}{2}})$.":[151],"Finally,":[152],"numerical":[153],"experiments":[154],"double-integrator":[157],"pursuit-evasion":[158],"illustrate":[160],"induced":[162],"physical":[163],"behaviors":[164],"validate":[166],"theoretical":[168],"bounds.":[169]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-02T00:00:00"}
