{"title":"On the Upper Bound of Near Potential Differential Games","authors":"Balint Varga","doi":"10.1016/j.rinam.2024.100453","DOIUrl":null,"url":null,"abstract":"<div><p>This letter presents an extended analysis and a novel upper bound of the subclass of Linear Quadratic Near Potential Differential Games (LQ NPDG). LQ NPDGs are a subclass of potential differential games, for which there is a distance between an LQ exact potential differential game and the LQ NPDG. LQ NPDGs exhibit a unique characteristic: The smaller the distance from an LQ exact potential differential game, the more closer their dynamic trajectories. This letter introduces a novel upper bound for this distance. Moreover, a linear relation between this distance and the resulting trajectory errors is established, opening the possibility for further application of LQ NPDGs.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"22 ","pages":"Article 100453"},"PeriodicalIF":1.4000,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000232/pdfft?md5=ab9c4fddd1098daffbde300c81a0c9f6&pid=1-s2.0-S2590037424000232-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Results in Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2590037424000232","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
This letter presents an extended analysis and a novel upper bound of the subclass of Linear Quadratic Near Potential Differential Games (LQ NPDG). LQ NPDGs are a subclass of potential differential games, for which there is a distance between an LQ exact potential differential game and the LQ NPDG. LQ NPDGs exhibit a unique characteristic: The smaller the distance from an LQ exact potential differential game, the more closer their dynamic trajectories. This letter introduces a novel upper bound for this distance. Moreover, a linear relation between this distance and the resulting trajectory errors is established, opening the possibility for further application of LQ NPDGs.
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