Optimizing LQR controllers: A comparative study

Q3 Mathematics Results in Control and Optimization Pub Date : 2024-02-04 DOI:10.1016/j.rico.2024.100387

Sanjay Joseph Chacko , Neeraj P.C. , Rajesh Joseph Abraham

{"title":"Optimizing LQR controllers: A comparative study","authors":"Sanjay Joseph Chacko , Neeraj P.C. , Rajesh Joseph Abraham","doi":"10.1016/j.rico.2024.100387","DOIUrl":null,"url":null,"abstract":"<div><p>Linear Quadratic Regulator is one of the most common ways to control a linear system. Despite Linear Quadratic Regulator’s (LQR) strong performance and solid resilience, developing these controllers have been challenging, largely because there is no reliable way to choose the <span><math><mi>Q</mi></math></span> and <span><math><mi>R</mi></math></span> weighing matrices. In this regard a deterministic method is used for choosing them in this paper, providing the designers a precise control over performance variables. An Artificial Bee Colony (ABC) optimisation is also used to find the sub-optimal gain matrices along with an analytical approach based on neural networks. A comparative study of the three approaches is performed using MATLAB simulations. These three approaches are applied on an inverted pendulum–cart system due to its complexity and dexterity. The results show that all the three methods show comparable performances with the proposed analytical method being slightly better in terms of transient characteristics.</p></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"14 ","pages":"Article 100387"},"PeriodicalIF":0.0000,"publicationDate":"2024-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666720724000171/pdfft?md5=73aba1c28b1ab24f0aeefaf53de0975b&pid=1-s2.0-S2666720724000171-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Results in Control and Optimization","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2666720724000171","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 0

Abstract

Linear Quadratic Regulator is one of the most common ways to control a linear system. Despite Linear Quadratic Regulator’s (LQR) strong performance and solid resilience, developing these controllers have been challenging, largely because there is no reliable way to choose the $Q$ and $R$ weighing matrices. In this regard a deterministic method is used for choosing them in this paper, providing the designers a precise control over performance variables. An Artificial Bee Colony (ABC) optimisation is also used to find the sub-optimal gain matrices along with an analytical approach based on neural networks. A comparative study of the three approaches is performed using MATLAB simulations. These three approaches are applied on an inverted pendulum–cart system due to its complexity and dexterity. The results show that all the three methods show comparable performances with the proposed analytical method being slightly better in terms of transient characteristics.

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

优化 LQR 控制器：比较研究

线性二次调节器是控制线性系统最常用的方法之一。尽管线性二次调节器（LQR）具有强大的性能和稳固的弹性，但开发这些控制器一直是一项挑战，主要是因为没有可靠的方法来选择 Q 和 R 权重矩阵。为此，本文采用了一种确定性方法来选择它们，为设计人员提供了对性能变量的精确控制。人工蜂群（ABC）优化法和基于神经网络的分析方法也用于寻找次优增益矩阵。通过 MATLAB 仿真对这三种方法进行了比较研究。由于倒立摆-小车系统的复杂性和灵巧性，这三种方法都被应用于该系统。结果表明，这三种方法的性能相当，而所提出的分析方法在瞬态特性方面略胜一筹。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文去求助

来源期刊