{"title":"基于数据的未知非仿射系统动态反馈近似最优控制","authors":"Jin-Jye Lin, Bo Zhao, Derong Liu","doi":"10.1109/DDCLS58216.2023.10166780","DOIUrl":null,"url":null,"abstract":"In this paper, an integral reinforcement learning (IRL)-based approximate optimal control (AOC) method for unknown nonaffine systems is developed by using dynamic feedback. For optimal control problems of nonaffine systems, optimal control policy cannot be expressed explicitly since the input gain matrix is unknown. Therefore, the nonaffine system is transformed into an augmented affine system by introducing a dynamic feedback signal as the virtual control input. Moreover, by designing an appropriate value function for the augmented affine system, the optimal control of augmented affine system is formulated as the AOC for unknown nonaffine systems. Moreover, the IRL method is adopted to derive the approximate solution of Hamilton-Jacobi-Bellman equation via the critic-only structure. Theoretical analysis concludes that the closed-loop system is uniformly ultimately bounded by using the developed IRL-based AOC scheme. An example is utilized to demonstrate the effectiveness of the present approach.","PeriodicalId":415532,"journal":{"name":"2023 IEEE 12th Data Driven Control and Learning Systems Conference (DDCLS)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Data-Based Approximate Optimal Control for Unknown Nonaffine Systems via Dynamic Feedback\",\"authors\":\"Jin-Jye Lin, Bo Zhao, Derong Liu\",\"doi\":\"10.1109/DDCLS58216.2023.10166780\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, an integral reinforcement learning (IRL)-based approximate optimal control (AOC) method for unknown nonaffine systems is developed by using dynamic feedback. For optimal control problems of nonaffine systems, optimal control policy cannot be expressed explicitly since the input gain matrix is unknown. Therefore, the nonaffine system is transformed into an augmented affine system by introducing a dynamic feedback signal as the virtual control input. Moreover, by designing an appropriate value function for the augmented affine system, the optimal control of augmented affine system is formulated as the AOC for unknown nonaffine systems. Moreover, the IRL method is adopted to derive the approximate solution of Hamilton-Jacobi-Bellman equation via the critic-only structure. Theoretical analysis concludes that the closed-loop system is uniformly ultimately bounded by using the developed IRL-based AOC scheme. An example is utilized to demonstrate the effectiveness of the present approach.\",\"PeriodicalId\":415532,\"journal\":{\"name\":\"2023 IEEE 12th Data Driven Control and Learning Systems Conference (DDCLS)\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-05-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2023 IEEE 12th Data Driven Control and Learning Systems Conference (DDCLS)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/DDCLS58216.2023.10166780\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2023 IEEE 12th Data Driven Control and Learning Systems Conference (DDCLS)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/DDCLS58216.2023.10166780","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Data-Based Approximate Optimal Control for Unknown Nonaffine Systems via Dynamic Feedback
In this paper, an integral reinforcement learning (IRL)-based approximate optimal control (AOC) method for unknown nonaffine systems is developed by using dynamic feedback. For optimal control problems of nonaffine systems, optimal control policy cannot be expressed explicitly since the input gain matrix is unknown. Therefore, the nonaffine system is transformed into an augmented affine system by introducing a dynamic feedback signal as the virtual control input. Moreover, by designing an appropriate value function for the augmented affine system, the optimal control of augmented affine system is formulated as the AOC for unknown nonaffine systems. Moreover, the IRL method is adopted to derive the approximate solution of Hamilton-Jacobi-Bellman equation via the critic-only structure. Theoretical analysis concludes that the closed-loop system is uniformly ultimately bounded by using the developed IRL-based AOC scheme. An example is utilized to demonstrate the effectiveness of the present approach.