{"title":"流体流动系统长时间平均成本控制的低阶状态反馈控制器设计:平方和方法","authors":"Deqing Huang, Chernyshenko Sergei","doi":"10.1109/CHICC.2015.7260020","DOIUrl":null,"url":null,"abstract":"This paper presents a novel state-feedback controller design approach for long-time average cost control of fluid flows. Due to the high dimensionality of fluid dynamical system, direct controller design renders to high-order state feedback that might not be applicable in practice. To resolve this, the original system is first transformed into a reduced-order uncertain system, where polynomial bounds for the involved uncertainties are evaluated analytically. Meanwhile, instead of minimizing the time-averaged cost itself, we use its upper bound as the objective function for controller design. Then, under the framework of sum-of-squares-based optimization, the control law and a tunable function similar to the Lyapunov function are optimized simultaneously. The inherent non-convexity of the optimization is overcome by assuming that the controller takes a small-feedback structure, which actually is a series in a small parameter with all the coefficients being finite-order polynomials of the reduced-order system state. The main characteristics of the induced controller lie in its low-order structure and robustness.","PeriodicalId":421276,"journal":{"name":"2015 34th Chinese Control Conference (CCC)","volume":"26 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Low-order state-feedback controller design for long-time average cost control of fluid flow systems: A sum-of-squares approach\",\"authors\":\"Deqing Huang, Chernyshenko Sergei\",\"doi\":\"10.1109/CHICC.2015.7260020\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper presents a novel state-feedback controller design approach for long-time average cost control of fluid flows. Due to the high dimensionality of fluid dynamical system, direct controller design renders to high-order state feedback that might not be applicable in practice. To resolve this, the original system is first transformed into a reduced-order uncertain system, where polynomial bounds for the involved uncertainties are evaluated analytically. Meanwhile, instead of minimizing the time-averaged cost itself, we use its upper bound as the objective function for controller design. Then, under the framework of sum-of-squares-based optimization, the control law and a tunable function similar to the Lyapunov function are optimized simultaneously. The inherent non-convexity of the optimization is overcome by assuming that the controller takes a small-feedback structure, which actually is a series in a small parameter with all the coefficients being finite-order polynomials of the reduced-order system state. The main characteristics of the induced controller lie in its low-order structure and robustness.\",\"PeriodicalId\":421276,\"journal\":{\"name\":\"2015 34th Chinese Control Conference (CCC)\",\"volume\":\"26 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-09-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2015 34th Chinese Control Conference (CCC)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CHICC.2015.7260020\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2015 34th Chinese Control Conference (CCC)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CHICC.2015.7260020","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Low-order state-feedback controller design for long-time average cost control of fluid flow systems: A sum-of-squares approach
This paper presents a novel state-feedback controller design approach for long-time average cost control of fluid flows. Due to the high dimensionality of fluid dynamical system, direct controller design renders to high-order state feedback that might not be applicable in practice. To resolve this, the original system is first transformed into a reduced-order uncertain system, where polynomial bounds for the involved uncertainties are evaluated analytically. Meanwhile, instead of minimizing the time-averaged cost itself, we use its upper bound as the objective function for controller design. Then, under the framework of sum-of-squares-based optimization, the control law and a tunable function similar to the Lyapunov function are optimized simultaneously. The inherent non-convexity of the optimization is overcome by assuming that the controller takes a small-feedback structure, which actually is a series in a small parameter with all the coefficients being finite-order polynomials of the reduced-order system state. The main characteristics of the induced controller lie in its low-order structure and robustness.