With accurate dynamic system parameters (embodied in self-awareness statements), a controller can provide precise signals for tracking desired state trajectories. If dynamic system parameters are initially guessed inaccurately, a learning method may be used to find the accurate parameters. In the deterministic artificial intelligence method, self-awareness statements are formed as mathematical expressions of the governing physics. When the nonlinear, coupled expressions are precisely parameterized as the product of known matrix components and unknown vectrix (i.e., an intermediate between a dyadic and a matrix in regression form) tracking errors may be projected onto the known matrix to update the unknown vectrix in an optimal form (in a two-norm sense). In this work, a modified learning method is proposed and proved to have global convergence of both state error and parameter estimation error. The modified learning method is compared with those in the prequels using simulation experiments of three-dimensional rigid body dynamic rotation motion. The achieved state error convergence using the modified approach is two magnitudes better than using the methods in the prequels.
{"title":"Novel learning for control of nonlinear spacecraft dynamics","authors":"Bo-Ruei Huang, Timothy Sands","doi":"10.59400/jam.v1i1.42","DOIUrl":"https://doi.org/10.59400/jam.v1i1.42","url":null,"abstract":"With accurate dynamic system parameters (embodied in self-awareness statements), a controller can provide precise signals for tracking desired state trajectories. If dynamic system parameters are initially guessed inaccurately, a learning method may be used to find the accurate parameters. In the deterministic artificial intelligence method, self-awareness statements are formed as mathematical expressions of the governing physics. When the nonlinear, coupled expressions are precisely parameterized as the product of known matrix components and unknown vectrix (i.e., an intermediate between a dyadic and a matrix in regression form) tracking errors may be projected onto the known matrix to update the unknown vectrix in an optimal form (in a two-norm sense). In this work, a modified learning method is proposed and proved to have global convergence of both state error and parameter estimation error. The modified learning method is compared with those in the prequels using simulation experiments of three-dimensional rigid body dynamic rotation motion. The achieved state error convergence using the modified approach is two magnitudes better than using the methods in the prequels.","PeriodicalId":495855,"journal":{"name":"Journal of AppliedMath","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136311269","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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