{"title":"Linear Quadratic Zonotopic Control of Switched Systems: Application to Autonomous Vehicle Path-Tracking","authors":"Shuang Zhang;Sara Ifqir;Vicenç Puig","doi":"10.1109/LCSYS.2024.3416069","DOIUrl":null,"url":null,"abstract":"This letter proposes a zonotopic approach for the state feedback control problem of a class of uncertain switched systems subject to unknown but bounded disturbances and measurement noises. The proposed approach is the zonotopic analogous case of the switched Linear Quadratic Gaussian (LQG) control, in which the feedback loop is closed using the optimal estimates of a Switched Zonotopic Kalman Filter (SZKF) leading to a Switched Linear Quadratic Zonotopic (SLQZ) control scheme. In this context, first, a SZKF with offline filter gains design is proposed so that the unmeasurable system states can be estimated. Then, to tackle the synthesis of the SZKF and the state feedback controller, separation principle is proved so that the computation of the optimal controller and estimator can be done separately by finding the solutions to a finite set of Linear Matrix Inequalities (LMIs). At last, a reference path tracking controller of the vehicle lateral dynamics is designed to demonstrate the validity and performance of the proposed method.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":null,"pages":null},"PeriodicalIF":2.4000,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Control Systems Letters","FirstCategoryId":"1085","ListUrlMain":"https://ieeexplore.ieee.org/document/10560008/","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
This letter proposes a zonotopic approach for the state feedback control problem of a class of uncertain switched systems subject to unknown but bounded disturbances and measurement noises. The proposed approach is the zonotopic analogous case of the switched Linear Quadratic Gaussian (LQG) control, in which the feedback loop is closed using the optimal estimates of a Switched Zonotopic Kalman Filter (SZKF) leading to a Switched Linear Quadratic Zonotopic (SLQZ) control scheme. In this context, first, a SZKF with offline filter gains design is proposed so that the unmeasurable system states can be estimated. Then, to tackle the synthesis of the SZKF and the state feedback controller, separation principle is proved so that the computation of the optimal controller and estimator can be done separately by finding the solutions to a finite set of Linear Matrix Inequalities (LMIs). At last, a reference path tracking controller of the vehicle lateral dynamics is designed to demonstrate the validity and performance of the proposed method.