{"id":"https://openalex.org/W7225150790","doi":"https://doi.org/10.1080/00207721.2026.2753636","title":"Reinforcement learning approach for optimal DoS attack power allocation: a WDSQL method","display_name":"Reinforcement learning approach for optimal DoS attack power allocation: a WDSQL method","publication_year":2026,"publication_date":"2026-11-02","ids":{"openalex":"https://openalex.org/W7225150790","doi":"https://doi.org/10.1080/00207721.2026.2753636"},"language":"en","primary_location":{"id":"doi:10.1080/00207721.2026.2753636","doi":"https://doi.org/10.1080/00207721.2026.2753636","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207721.2026.2753636","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-d","jufo-1","norway-1","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Systems Science","raw_type":"journal-article"},"volume":null,"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/A5160400330","display_name":"Jing Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I143593769","display_name":"East China University of Science and Technology","ror":"https://ror.org/01vyrm377","country_code":"CN","type":"education","lineage":["https://openalex.org/I143593769"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jing Liu","raw_affiliation_strings":["East China University of Science and Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"East China University of Science and Technology","institution_ids":["https://openalex.org/I143593769"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5160484592","display_name":"Xiaolin Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I143593769","display_name":"East China University of Science and Technology","ror":"https://ror.org/01vyrm377","country_code":"CN","type":"education","lineage":["https://openalex.org/I143593769"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiaolin Wang","raw_affiliation_strings":["East China University of Science and Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"East China University of Science and Technology","institution_ids":["https://openalex.org/I143593769"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5160362072","display_name":"Junhui Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Junhui Zhang","raw_affiliation_strings":["The School of Robotics and Automation, Nanjing University, Suzhou, Jiangsu, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The School of Robotics and Automation, Nanjing University, Suzhou, Jiangsu, People's Republic of China","institution_ids":["https://openalex.org/I881766915"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100763314","display_name":"Fangfei Li","orcid":"https://orcid.org/0000-0001-7978-8125","observed_orcids":["https://orcid.org/0000-0001-7978-8125"]},"institutions":[{"id":"https://openalex.org/I143593769","display_name":"East China University of Science and Technology","ror":"https://ror.org/01vyrm377","country_code":"CN","type":"education","lineage":["https://openalex.org/I143593769"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Fangfei Li","raw_affiliation_strings":["East China University of Science and Technology","State Key Laboratory of Industrial Control Technology, East China University of Science and Technology, Shanghai, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"East China University of Science and Technology","institution_ids":["https://openalex.org/I143593769"]},{"raw_affiliation_string":"State Key Laboratory of Industrial Control Technology, East China University of Science and Technology, Shanghai, People's Republic of China","institution_ids":["https://openalex.org/I143593769"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100763314","https://openalex.org/A5160484592"],"corresponding_institution_ids":["https://openalex.org/I143593769"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.80214928,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"19"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10917","display_name":"Smart Grid Security and Resilience","score":0.8920999765396118,"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/T10917","display_name":"Smart Grid Security and Resilience","score":0.8920999765396118,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.044599998742341995,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.008899999782443047,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/denial-of-service-attacks","display_name":"denial-of-service attacks","score":0.8740000128746033},{"id":"https://openalex.org/keywords/cyber-physical-systems","display_name":"cyber-physical systems","score":0.9200000166893005},{"id":"https://openalex.org/keywords/markov-decision-process","display_name":"Markov decision process","score":0.7120000123977661},{"id":"https://openalex.org/keywords/model-free-reinforcement-learning","display_name":"model-free reinforcement learning","score":0.8939999938011169},{"id":"https://openalex.org/keywords/nonlinear-systems","display_name":"nonlinear systems","score":0.5320000052452087},{"id":"https://openalex.org/keywords/covariance-propagation","display_name":"covariance propagation","score":0.5879999995231628},{"id":"https://openalex.org/keywords/almost-sure-convergence","display_name":"almost sure convergence","score":0.7099999785423279},{"id":"https://openalex.org/keywords/conditional-stability","display_name":"conditional stability","score":0.6809999942779541},{"id":"https://openalex.org/keywords/target-tracking","display_name":"target tracking","score":0.7329999804496765},{"id":"https://openalex.org/keywords/proactive-defense","display_name":"proactive defense","score":0.6919999718666077}],"concepts":[{"id":"https://openalex.org/C106189395","wikidata":"https://www.wikidata.org/wiki/Q176789","display_name":"Markov decision process","level":3,"score":0.6549999713897705},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6193000078201294},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5942000150680542},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5673999786376953},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.552299976348877},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.5181000232696533},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5153999924659729},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4957999885082245},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.45719999074935913},{"id":"https://openalex.org/C157286648","wikidata":"https://www.wikidata.org/wiki/Q846780","display_name":"Kalman filter","level":2,"score":0.42329999804496765},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.4171000123023987},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.4074999988079071},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.38350000977516174},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.366100013256073},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.3644999861717224},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34850001335144043},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.30550000071525574},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.296999990940094},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.29019999504089355},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.28839999437332153},{"id":"https://openalex.org/C183560197","wikidata":"https://www.wikidata.org/wiki/Q7247302","display_name":"Process state","level":3,"score":0.2720000147819519},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.25870001316070557},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.25130000710487366}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207721.2026.2753636","doi":"https://doi.org/10.1080/00207721.2026.2753636","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207721.2026.2753636","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-d","jufo-1","norway-1","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Systems Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W32403112","https://openalex.org/W1651728063","https://openalex.org/W1804494423","https://openalex.org/W1987806716","https://openalex.org/W2003530067","https://openalex.org/W2012005963","https://openalex.org/W2038331462","https://openalex.org/W2047719998","https://openalex.org/W2063688797","https://openalex.org/W2107043025","https://openalex.org/W2132902886","https://openalex.org/W2140439200","https://openalex.org/W2145339207","https://openalex.org/W2165131254","https://openalex.org/W2167489871","https://openalex.org/W2286561681","https://openalex.org/W2324627801","https://openalex.org/W2336416123","https://openalex.org/W2340384825","https://openalex.org/W2525975698","https://openalex.org/W2581108373","https://openalex.org/W2740912559","https://openalex.org/W2758737610","https://openalex.org/W2778403987","https://openalex.org/W2792059154","https://openalex.org/W2897746747","https://openalex.org/W2926535828","https://openalex.org/W2943560396","https://openalex.org/W2963510622","https://openalex.org/W2972470616","https://openalex.org/W3002997336","https://openalex.org/W3012541498","https://openalex.org/W3036062693","https://openalex.org/W3045798462","https://openalex.org/W3112645336","https://openalex.org/W3129797436","https://openalex.org/W3161310610","https://openalex.org/W3161801274","https://openalex.org/W3162437935","https://openalex.org/W3175323262","https://openalex.org/W4224862297","https://openalex.org/W4285585442","https://openalex.org/W4288049701","https://openalex.org/W4294300376","https://openalex.org/W4308822543","https://openalex.org/W4312411344","https://openalex.org/W4316660617","https://openalex.org/W4385980686","https://openalex.org/W4400123103","https://openalex.org/W4405037471","https://openalex.org/W4409723779","https://openalex.org/W4410441312","https://openalex.org/W4412170773","https://openalex.org/W4413155480","https://openalex.org/W7117478912"],"related_works":["https://openalex.org/W4212838699","https://openalex.org/W4390894093","https://openalex.org/W3202785310","https://openalex.org/W4313839174","https://openalex.org/W4321499269","https://openalex.org/W4224862297","https://openalex.org/W4285260764","https://openalex.org/W2961090905","https://openalex.org/W4405718185","https://openalex.org/W4285732625"],"abstract_inverted_index":{"This":[0],"paper":[1],"develops":[2],"an":[3,150],"optimal":[4],"denial-of-service":[5],"(DoS)":[6],"attack":[7,172,203],"strategy":[8],"for":[9,49],"cyber-physical":[10],"systems":[11,26],"(CPS)":[12],"under":[13,125,149,187],"power":[14,68],"constraints":[15],"and":[16,59,90,110,113,127,130,134,142,146,179],"limited":[17],"prior":[18,21],"knowledge.":[19],"Unlike":[20],"works":[22],"that":[23,71,167],"assume":[24],"linear":[25],"with":[27,154],"steady-state":[28],"Kalman":[29],"filter":[30],"convergence,":[31],"we":[32],"consider":[33],"a":[34,67,77,85,92,102,155,161,180],"nonlinear":[35],"system":[36],"in":[37,138],"which":[38],"the":[39,45,131,139,170,175,188,197],"attacker":[40],"has":[41],"partial":[42],"knowledge":[43],"of":[44,200],"physical":[46],"dynamics":[47],"required":[48],"covariance":[50],"propagation,":[51],"observes":[52],"ACK":[53],"signals,":[54],"but":[55],"lacks":[56],"wireless-channel":[57],"information":[58],"transition":[60],"probabilities.":[61],"The":[62],"objective":[63],"is":[64],"to":[65,106,118],"learn":[66],"allocation":[69],"policy":[70],"maximises":[72],"estimation":[73],"performance":[74],"degradation":[75],"over":[76],"finite":[78],"horizon.":[79],"We":[80,121],"formulate":[81],"this":[82],"problem":[83],"as":[84],"Markov":[86],"decision":[87],"process":[88],"(MDP)":[89],"propose":[91],"model-free":[93],"algorithm,":[94],"weighted":[95,103],"double":[96,104],"speedy":[97],"Q-learning":[98],"(WDSQL).":[99],"WDSQL":[100,168],"employs":[101],"estimator":[105],"balance":[107],"both":[108],"overestimation":[109],"underestimation":[111],"biases,":[112],"incorporates":[114],"auxiliary":[115],"memory":[116],"functions":[117],"accelerate":[119],"convergence.":[120],"establish":[122],"almost-sure":[123],"convergence":[124,140],"finite-state":[126],"infinite-visitation":[128],"assumptions":[129],"learning-rate,":[132],"conditional-expectation,":[133],"conditional-variance":[135],"conditions":[136],"stated":[137],"analysis,":[141],"derive":[143],"conditional":[144],"stability":[145],"error-propagation":[147],"bounds":[148],"additional":[151],"boundedness":[152],"condition,":[153],"computational":[156],"complexity":[157],"analysis.":[158],"Simulations":[159],"on":[160],"dynamic":[162],"target":[163],"tracking":[164],"scenario":[165],"show":[166],"achieves":[169],"highest":[171],"effectiveness":[173],"among":[174],"compared":[176],"RL":[177],"methods":[178],"lower":[181],"empirical":[182],"running":[183],"time":[184],"than":[185],"DQN":[186],"tested":[189],"setting.":[190],"A":[191],"proactive":[192],"defense":[193],"experiment":[194],"further":[195],"highlights":[196],"practical":[198],"value":[199],"understanding":[201],"learning-based":[202],"strategies.":[204]},"counts_by_year":[],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2026-11-04T00:00:00"}