{"title":"非线性系统的梯度-后裔迭代学习控制算法","authors":"Zhi-ying He, Hongji Pu","doi":"10.1177/01423312241247873","DOIUrl":null,"url":null,"abstract":"Original iterative learning control (OILC) has been proved a powerful tool in dealing with the model-free control problems by repetitively corrections based on the control error. However, the steady-state error under widely-used proportional-type original iterative learning control (P-type OILC) is highly corresponded to the proportional learning gain, making the algorithm parameter-determined. Therefore, a new gradient-descent iterative learning control (GDILC) algorithm is proposed to achieve a parameter-free approach by simulating the gradient-descent process. First, GDILC problem is formulated mathematically. Next, the idea of the algorithm is proposed, the analyses of the convergence and the steady-state error are conducted and the algorithm is implemented. GDILC will generate a random correction with a gradient-descent upper bound, rather than a correction proportional to the error in P-type OILC. Finally, illustrative and application simulations are conducted to validate the algorithm. Results show that the algorithm will be convergent after adequate iterations under proper corrections. The steady-state error will be less affected by the algorithm parameters under GDILC than that under OILC.","PeriodicalId":49426,"journal":{"name":"Transactions of the Institute of Measurement and Control","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A gradient-descent iterative learning control algorithm for a non-linear system\",\"authors\":\"Zhi-ying He, Hongji Pu\",\"doi\":\"10.1177/01423312241247873\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Original iterative learning control (OILC) has been proved a powerful tool in dealing with the model-free control problems by repetitively corrections based on the control error. However, the steady-state error under widely-used proportional-type original iterative learning control (P-type OILC) is highly corresponded to the proportional learning gain, making the algorithm parameter-determined. Therefore, a new gradient-descent iterative learning control (GDILC) algorithm is proposed to achieve a parameter-free approach by simulating the gradient-descent process. First, GDILC problem is formulated mathematically. Next, the idea of the algorithm is proposed, the analyses of the convergence and the steady-state error are conducted and the algorithm is implemented. GDILC will generate a random correction with a gradient-descent upper bound, rather than a correction proportional to the error in P-type OILC. Finally, illustrative and application simulations are conducted to validate the algorithm. Results show that the algorithm will be convergent after adequate iterations under proper corrections. The steady-state error will be less affected by the algorithm parameters under GDILC than that under OILC.\",\"PeriodicalId\":49426,\"journal\":{\"name\":\"Transactions of the Institute of Measurement and Control\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-05-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions of the Institute of Measurement and Control\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1177/01423312241247873\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of the Institute of Measurement and Control","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1177/01423312241247873","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
A gradient-descent iterative learning control algorithm for a non-linear system
Original iterative learning control (OILC) has been proved a powerful tool in dealing with the model-free control problems by repetitively corrections based on the control error. However, the steady-state error under widely-used proportional-type original iterative learning control (P-type OILC) is highly corresponded to the proportional learning gain, making the algorithm parameter-determined. Therefore, a new gradient-descent iterative learning control (GDILC) algorithm is proposed to achieve a parameter-free approach by simulating the gradient-descent process. First, GDILC problem is formulated mathematically. Next, the idea of the algorithm is proposed, the analyses of the convergence and the steady-state error are conducted and the algorithm is implemented. GDILC will generate a random correction with a gradient-descent upper bound, rather than a correction proportional to the error in P-type OILC. Finally, illustrative and application simulations are conducted to validate the algorithm. Results show that the algorithm will be convergent after adequate iterations under proper corrections. The steady-state error will be less affected by the algorithm parameters under GDILC than that under OILC.
期刊介绍:
Transactions of the Institute of Measurement and Control is a fully peer-reviewed international journal. The journal covers all areas of applications in instrumentation and control. Its scope encompasses cutting-edge research and development, education and industrial applications.