{"id":"https://openalex.org/W7225797766","doi":"https://doi.org/10.3390/math14224147","title":"Mathematical Modelling and Lyapunov Stability Analysis of Solar-Powered Recirculating-Water Gravity Energy Storage Systems Under False Data Injection Attacks","display_name":"Mathematical Modelling and Lyapunov Stability Analysis of Solar-Powered Recirculating-Water Gravity Energy Storage Systems Under False Data Injection Attacks","publication_year":2026,"publication_date":"2026-11-11","ids":{"openalex":"https://openalex.org/W7225797766","doi":"https://doi.org/10.3390/math14224147"},"language":"en","primary_location":{"id":"doi:10.3390/math14224147","doi":"https://doi.org/10.3390/math14224147","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math14224147","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/math14224147","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159167884","display_name":"Okafor Wisdom Onyema","orcid":"https://orcid.org/0009-0005-6122-7844","observed_orcids":["https://orcid.org/0009-0005-6122-7844"]},"institutions":[{"id":"https://openalex.org/I104658917","display_name":"University of Chichester","ror":"https://ror.org/029tw2407","country_code":"GB","type":"education","lineage":["https://openalex.org/I104658917"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Wisdom Onyema Okafor","raw_affiliation_strings":["CPRE London, London EC1M 6EJ, UK","IEEE Skill Up Hub, University of Chichester, Region 8, Bognor Regis PO21 1HR, UK"],"raw_orcid":"https://orcid.org/0009-0005-6122-7844","affiliations":[{"raw_affiliation_string":"CPRE London, London EC1M 6EJ, UK","institution_ids":[]},{"raw_affiliation_string":"IEEE Skill Up Hub, University of Chichester, Region 8, Bognor Regis PO21 1HR, UK","institution_ids":["https://openalex.org/I104658917"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5161463047","display_name":"Chinyere P. Okafor","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I166934088","display_name":"Imo State University","ror":"https://ror.org/0257ekp23","country_code":"NG","type":"education","lineage":["https://openalex.org/I166934088"]}],"countries":["NG"],"is_corresponding":false,"raw_author_name":"Chinyere P. Okafor","raw_affiliation_strings":["Department of Mathematics Education, Imo State University, Owerri 460108, Nigeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Education, Imo State University, Owerri 460108, Nigeria","institution_ids":["https://openalex.org/I166934088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5161428520","display_name":"Esther Chioma Nnaleche","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I147554453","display_name":"University of Bedfordshire","ror":"https://ror.org/0400avk24","country_code":"GB","type":"education","lineage":["https://openalex.org/I147554453"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Esther Chioma Nnaleche","raw_affiliation_strings":["Department of Cybersecurity, University of Bedfordshire, Luton LU1 3JU, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Cybersecurity, University of Bedfordshire, Luton LU1 3JU, UK","institution_ids":["https://openalex.org/I147554453"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047509158","display_name":"Joshua Chukwu","orcid":"https://orcid.org/0000-0002-5814-1397","observed_orcids":["https://orcid.org/0000-0002-5814-1397"]},"institutions":[{"id":"https://openalex.org/I147554453","display_name":"University of Bedfordshire","ror":"https://ror.org/0400avk24","country_code":"GB","type":"education","lineage":["https://openalex.org/I147554453"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Joshua Chukwu","raw_affiliation_strings":["Information Technology, University of Bedfordshire, Luton LU1 3JU, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Information Technology, University of Bedfordshire, Luton LU1 3JU, UK","institution_ids":["https://openalex.org/I147554453"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011425554","display_name":"Kelvin Anoh","orcid":"https://orcid.org/0000-0002-2538-6945","observed_orcids":["https://orcid.org/0000-0002-2538-6945"]},"institutions":[{"id":"https://openalex.org/I104658917","display_name":"University of Chichester","ror":"https://ror.org/029tw2407","country_code":"GB","type":"education","lineage":["https://openalex.org/I104658917"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Kelvin Anoh","raw_affiliation_strings":["Center for Future Technologies, University of Chichester, Bognor Regis PO21 1HR, UK","IEEE Skill Up Hub, University of Chichester, Region 8, Bognor Regis PO21 1HR, UK"],"raw_orcid":"https://orcid.org/0000-0002-2538-6945","affiliations":[{"raw_affiliation_string":"Center for Future Technologies, University of Chichester, Bognor Regis PO21 1HR, UK","institution_ids":["https://openalex.org/I104658917"]},{"raw_affiliation_string":"IEEE Skill Up Hub, University of Chichester, Region 8, Bognor Regis PO21 1HR, UK","institution_ids":["https://openalex.org/I104658917"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055990328","display_name":"Omowunmi Mary Longe","orcid":"https://orcid.org/0000-0002-2170-7289","observed_orcids":["https://orcid.org/0000-0002-2170-7289"]},"institutions":[{"id":"https://openalex.org/I24027795","display_name":"University of Johannesburg","ror":"https://ror.org/04z6c2n17","country_code":"ZA","type":"education","lineage":["https://openalex.org/I24027795"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Omowunmi Mary Longe","raw_affiliation_strings":["Department of Electrical and Electronic Engineering Science, University of Johannesburg, Johannesburg 2006, South Africa"],"raw_orcid":"https://orcid.org/0000-0002-2170-7289","affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering Science, University of Johannesburg, Johannesburg 2006, South Africa","institution_ids":["https://openalex.org/I24027795"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077937102","display_name":"Kennedy Chinedu Okafor","orcid":"https://orcid.org/0000-0002-9243-6789","observed_orcids":["https://orcid.org/0000-0002-9243-6789"]},"institutions":[{"id":"https://openalex.org/I104658917","display_name":"University of Chichester","ror":"https://ror.org/029tw2407","country_code":"GB","type":"education","lineage":["https://openalex.org/I104658917"]},{"id":"https://openalex.org/I4405260661","display_name":"Federal University of Allied Health Sciences, Enugu","ror":"https://ror.org/043gg8967","country_code":"NG","type":"education","lineage":["https://openalex.org/I4405260661"]}],"countries":["GB","NG"],"is_corresponding":false,"raw_author_name":"Kennedy Chinedu Okafor","raw_affiliation_strings":["Center for Future Technologies, University of Chichester, Bognor Regis PO21 1HR, UK","Department of Software Engineering, Federal University of Allied Health Sciences, Enugu (FUAHSE), Enugu 400103, Nigeria","IEEE Skill Up Hub, University of Chichester, Region 8, Bognor Regis PO21 1HR, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Future Technologies, University of Chichester, Bognor Regis PO21 1HR, UK","institution_ids":["https://openalex.org/I104658917"]},{"raw_affiliation_string":"Department of Software Engineering, Federal University of Allied Health Sciences, Enugu (FUAHSE), Enugu 400103, Nigeria","institution_ids":["https://openalex.org/I4405260661"]},{"raw_affiliation_string":"IEEE Skill Up Hub, University of Chichester, Region 8, Bognor Regis PO21 1HR, UK","institution_ids":["https://openalex.org/I104658917"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5159167884"],"corresponding_institution_ids":["https://openalex.org/I104658917"],"apc_list":{"value":2600,"currency":"CHF","value_usd":3137},"apc_paid":{"value":2600,"currency":"CHF","value_usd":3137},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"22","first_page":"4147","last_page":"4147"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10917","display_name":"Smart Grid Security and Resilience","score":0.9980000257492065,"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":0.9980000257492065,"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/T10305","display_name":"Power System Optimization and Stability","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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":9.999999747378752e-05,"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":[],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7322999835014343},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5291000008583069},{"id":"https://openalex.org/C2776829284","wikidata":"https://www.wikidata.org/wiki/Q1341651","display_name":"Lyapunov stability","level":3,"score":0.5185999870300293},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.48159998655319214},{"id":"https://openalex.org/C73916439","wikidata":"https://www.wikidata.org/wiki/Q837718","display_name":"Energy storage","level":3,"score":0.46480000019073486},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.45500001311302185},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.398499995470047},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.3792000114917755},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3619999885559082},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.36000001430511475},{"id":"https://openalex.org/C2780704645","wikidata":"https://www.wikidata.org/wiki/Q9251458","display_name":"Observer (physics)","level":2,"score":0.3321000039577484},{"id":"https://openalex.org/C94915269","wikidata":"https://www.wikidata.org/wiki/Q1834857","display_name":"Detector","level":2,"score":0.3273000121116638},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.3255999982357025},{"id":"https://openalex.org/C2778449969","wikidata":"https://www.wikidata.org/wiki/Q130760","display_name":"Turbine","level":2,"score":0.31150001287460327},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.29589998722076416},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.27639999985694885},{"id":"https://openalex.org/C2780165032","wikidata":"https://www.wikidata.org/wiki/Q16869822","display_name":"Energy consumption","level":2,"score":0.2705000042915344},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.26739999651908875},{"id":"https://openalex.org/C20556612","wikidata":"https://www.wikidata.org/wiki/Q4469374","display_name":"Volume (thermodynamics)","level":2,"score":0.25839999318122864},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.251800000667572}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/math14224147","doi":"https://doi.org/10.3390/math14224147","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math14224147","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3390/math14224147","doi":"https://doi.org/10.3390/math14224147","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math14224147","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Solar-powered":[0],"recirculating-water":[1],"gravity":[2,36],"energy":[3,13,17],"storage":[4,9,37,48],"(SRWGES)":[5],"is":[6,27,114,136,156,217,227],"a":[7,63,68,80,91,110,132,142,151,179,198,205,222],"electromechanical":[8],"technology":[10],"that":[11,55,77,122,170],"holds":[12],"as":[14,102],"gravitational":[15],"potential":[16],"of":[18,47,67,147,215],"water,":[19],"yet":[20],"its":[21],"digital":[22],"sensing":[23],"and":[24,42,52,96,126,131,161,191,220,224],"control":[25],"layer":[26],"exposed":[28],"to":[29,116,138,186],"false":[30],"data":[31],"injection":[32],"(FDI)":[33],"attacks.":[34],"Existing":[35],"research":[38],"addresses":[39],"sizing,":[40],"economics":[41],"dispatch,":[43],"while":[44],"cybersecurity":[45],"studies":[46],"concentrate":[49],"on":[50,53],"batteries":[51],"detectors":[54],"ignore":[56],"plant":[57,70],"dynamics.":[58],"No":[59],"earlier":[60],"study":[61],"provides":[62],"physics-based":[64,180],"stability":[65,98,226],"analysis":[66],"gravity-storage":[69],"under":[71,189],"adversarial":[72],"sensing.":[73],"This":[74],"paper":[75],"closes":[76],"gap":[78],"with":[79,163],"four-state":[81],"nonlinear":[82,164],"model":[83],"whose":[84],"turbine":[85],"generator":[86],"dynamics":[87],"are":[88,100,107,211],"derived":[89,157],"from":[90],"torque":[92],"balance.":[93],"Established":[94],"Lyapunov":[95],"input-to-state":[97],"tools":[99],"used":[101],"such.":[103],"The":[104],"original":[105],"contributions":[106],"three.":[108],"First,":[109],"proportional-only":[111],"flow":[112,127],"governor":[113],"shown":[115,137],"produce":[117],"an":[118,218],"exact,":[119],"parameter-independent":[120],"cancellation":[121],"leaves":[123],"the":[124,183,213],"speed":[125,133],"subsystem":[128],"marginally":[129],"stable,":[130],"droop":[134],"term":[135],"remove":[139],"it.":[140],"Second,":[141],"closed-form":[143],"attack":[144],"tolerance":[145],"threshold":[146,200],"20.16":[148],"m3":[149,153,188],"for":[150],"20":[152],"safety":[154],"margin":[155],"in":[158],"physical":[159],"parameters":[160],"agrees":[162],"simulation":[165],"within":[166],"0.6%;":[167],"it":[168],"shows":[169],"tighter":[171],"proportional":[172],"regulation":[173],"does":[174],"not":[175,221,228],"improve":[176],"resilience.":[177],"Third,":[178],"observer":[181],"limits":[182],"volume":[184],"deviation":[185],"1.31":[187],"single":[190],"coordinated":[192],"attacks,":[193],"whereas,":[194],"without":[195],"measurement":[196],"noise,":[197],"raw":[199],"detector":[201],"never":[202],"alarms":[203],"against":[204],"constructed":[206],"masking":[207],"attack.":[208],"Stability":[209],"results":[210],"local,":[212],"region":[214],"attraction":[216],"estimate":[219],"certificate,":[223],"global":[225],"claimed.":[229]},"counts_by_year":[],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2026-11-12T00:00:00"}