{"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}
引用次数: 1
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.