{"id":"https://openalex.org/W7207870852","doi":"https://doi.org/10.48550/arxiv.2609.02363","title":"On the invariance of risk-sensitive LQR gain under input randomization","display_name":"On the invariance of risk-sensitive LQR gain under input randomization","publication_year":2026,"publication_date":"2026-09-02","ids":{"openalex":"https://openalex.org/W7207870852","doi":"https://doi.org/10.48550/arxiv.2609.02363"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.02363","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02363","pdf_url":"https://arxiv.org/pdf/2609.02363","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.02363","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078952614","display_name":"Yeongjun Jang","orcid":"https://orcid.org/0009-0007-0784-0212","observed_orcids":["https://orcid.org/0009-0007-0784-0212"]},"institutions":[{"id":"https://openalex.org/I139264467","display_name":"Seoul National University","ror":"https://ror.org/04h9pn542","country_code":"KR","type":"education","lineage":["https://openalex.org/I139264467"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Jang, Yeongjun","raw_affiliation_strings":["ASRI , Department of Electrical and Computer Engineering , Seoul National University , Seoul , 08826 , Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ASRI , Department of Electrical and Computer Engineering , Seoul National University , Seoul , 08826 , Korea","institution_ids":["https://openalex.org/I139264467"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5078952614"],"corresponding_institution_ids":["https://openalex.org/I139264467"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.7900000214576721,"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":0.7900000214576721,"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/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.07590000331401825,"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":0.07289999723434448,"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/optimal-control-gain","display_name":"optimal control gain","score":0.6890000104904175},{"id":"https://openalex.org/keywords/invariance","display_name":"invariance","score":0.7360000014305115},{"id":"https://openalex.org/keywords/certainty-equivalence","display_name":"certainty equivalence","score":0.7279999852180481},{"id":"https://openalex.org/keywords/riccati-recursion","display_name":"Riccati recursion","score":0.7829999923706055},{"id":"https://openalex.org/keywords/input-noise","display_name":"input noise","score":0.628000020980835},{"id":"https://openalex.org/keywords/privacy-preserving-control","display_name":"privacy-preserving control","score":0.6119999885559082},{"id":"https://openalex.org/keywords/dynamic-watermarking","display_name":"dynamic watermarking","score":0.8659999966621399},{"id":"https://openalex.org/keywords/replay-attack-detection","display_name":"replay attack detection","score":0.9990000128746033}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7088000178337097},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.5726000070571899},{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.5633000135421753},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5422000288963318},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4925999939441681},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.4862000048160553},{"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/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.45019999146461487},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.4228000044822693},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3864000141620636},{"id":"https://openalex.org/C204495892","wikidata":"https://www.wikidata.org/wiki/Q1798304","display_name":"Linear-quadratic-Gaussian control","level":3,"score":0.36820000410079956},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.36640000343322754},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36340001225471497},{"id":"https://openalex.org/C183816354","wikidata":"https://www.wikidata.org/wiki/Q665617","display_name":"Infinite impulse response","level":4,"score":0.33660000562667847},{"id":"https://openalex.org/C36299963","wikidata":"https://www.wikidata.org/wiki/Q1369844","display_name":"Observability","level":2,"score":0.3280999958515167},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.32269999384880066},{"id":"https://openalex.org/C97090092","wikidata":"https://www.wikidata.org/wiki/Q764612","display_name":"Gain scheduling","level":3,"score":0.3192000091075897},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.3142000138759613},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.3052999973297119},{"id":"https://openalex.org/C87698059","wikidata":"https://www.wikidata.org/wiki/Q1808960","display_name":"LTI system theory","level":3,"score":0.30239999294281006},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2971999943256378},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.2962999939918518},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.2953000068664551},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.29120001196861267},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.27970001101493835},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.265500009059906},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.25940001010894775},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.25870001316070557}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.02363","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02363","pdf_url":"https://arxiv.org/pdf/2609.02363","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.02363","doi":"https://doi.org/10.48550/arxiv.2609.02363","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.02363","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,"listed_in":[],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.02363","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02363","pdf_url":"https://arxiv.org/pdf/2609.02363","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G506291142","display_name":null,"funder_award_id":"RS-2024-00353032","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"}],"funders":[{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"},{"id":"https://openalex.org/F4320328359","display_name":"Ministry of Science and ICT, South Korea","ror":"https://ror.org/01wpjm123"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7207870852.pdf","grobid_xml":"https://content.openalex.org/works/W7207870852.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7167573523"],"related_works":["https://openalex.org/W2275919383","https://openalex.org/W2482395990","https://openalex.org/W2187973349","https://openalex.org/W7220728640","https://openalex.org/W4408156221","https://openalex.org/W2101783086","https://openalex.org/W3015326182","https://openalex.org/W2143029398","https://openalex.org/W7033660020","https://openalex.org/W1589395967"],"abstract_inverted_index":{"This":[0,28,104],"paper":[1],"shows":[2],"that":[3,114],"the":[4,8,21,24,48,53,58,64,69,79,83,91,94,107],"optimal":[5,80,95],"gain":[6,54,81],"of":[7,109],"risk-sensitive":[9,42,110],"linear":[10],"quadratic":[11],"regulator":[12],"(LQR)":[13],"problem":[14],"is":[15,55],"invariant":[16],"under":[17],"input":[18,45,59,116],"randomization":[19,46,117],"when":[20],"cost":[22,70,96],"penalizes":[23],"realized":[25],"noisy":[26],"input.":[27],"may":[29],"appear":[30],"counterintuitive":[31],"at":[32],"first":[33],"glance":[34],"because":[35,57],"certainty":[36],"equivalence":[37],"does":[38],"not":[39,62,87],"hold":[40],"for":[41,118,126],"LQR":[43,111],"and":[44,72,82,90],"inflates":[47],"effective":[49],"process":[50],"noise.":[51],"Nonetheless,":[52],"preserved":[56],"noise":[60],"enters":[61],"only":[63],"system":[65],"dynamics":[66],"but":[67],"also":[68],"functional,":[71],"its":[73],"total":[74],"effect":[75],"eventually":[76],"vanishes.":[77],"Consequently,":[78],"Riccati":[84],"recursion":[85],"need":[86],"be":[88,98],"recomputed,":[89],"increment":[92],"in":[93,101,112],"can":[97],"readily":[99],"evaluated":[100],"closed":[102],"form.":[103],"result":[105],"facilitates":[106],"use":[108],"applications":[113],"employ":[115],"privacy":[119],"or":[120],"exploration,":[121],"such":[122],"as":[123],"dynamic":[124],"watermarking":[125],"replay":[127],"attack":[128],"detection.":[129]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-04T00:00:00"}