{"title":"一类非线性奇摄动系统的近最优反馈镇定","authors":"J. Chow, P. Kokotovic","doi":"10.1109/CDC.1978.267942","DOIUrl":null,"url":null,"abstract":"The problem considered is to optimally control the nonlinear system: x = a1(x) + A1(x)z + B1(x)u, x(0) = xo (1a) µz = a2(x) + A2(x)z + B2(x)u, z(0) = zo (1b) with respect to the performance index J=¿0 ¿[p(x) + s'(x)z + z'Q(x)z + u'R(x)u]dt (2) where µ > 0 is the small singular perturbation parameter, x, z are n-, m- dimensional states, respectively, and u is an r-dimensional control.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"28 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1978-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"35","resultStr":"{\"title\":\"Near-optimal feedback stabilization of a class of nonlinear singularly perturbed systems\",\"authors\":\"J. Chow, P. Kokotovic\",\"doi\":\"10.1109/CDC.1978.267942\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The problem considered is to optimally control the nonlinear system: x = a1(x) + A1(x)z + B1(x)u, x(0) = xo (1a) µz = a2(x) + A2(x)z + B2(x)u, z(0) = zo (1b) with respect to the performance index J=¿0 ¿[p(x) + s'(x)z + z'Q(x)z + u'R(x)u]dt (2) where µ > 0 is the small singular perturbation parameter, x, z are n-, m- dimensional states, respectively, and u is an r-dimensional control.\",\"PeriodicalId\":375119,\"journal\":{\"name\":\"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes\",\"volume\":\"28 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1978-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"35\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CDC.1978.267942\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.1978.267942","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 35
摘要
考虑的问题是最优控制非线性系统:x = a1(x) + a1(x) z + B1(x)u, x(0) = xo (1a)µz = a2(x) + a2(x) z + B2(x)u, z(0) = zo (1b)，相对于性能指标J=¿0¿[p(x) + s'(x)z + z' q (x)z + u' r (x)u]dt(2)，其中µ> 0是小奇异扰动参数，x, z分别是n维，m维状态，u是r维控制。
Near-optimal feedback stabilization of a class of nonlinear singularly perturbed systems
The problem considered is to optimally control the nonlinear system: x = a1(x) + A1(x)z + B1(x)u, x(0) = xo (1a) µz = a2(x) + A2(x)z + B2(x)u, z(0) = zo (1b) with respect to the performance index J=¿0 ¿[p(x) + s'(x)z + z'Q(x)z + u'R(x)u]dt (2) where µ > 0 is the small singular perturbation parameter, x, z are n-, m- dimensional states, respectively, and u is an r-dimensional control.
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