{"title":"Optimal Control for Simple Linear Hybrid Systems","authors":"Mahmoud A. A. Mousa, S. Schewe, D. Wojtczak","doi":"10.1109/TIME.2016.9","DOIUrl":null,"url":null,"abstract":"This paper studies optimal time-bounded control in a simple subclass of linear hybrid systems, which consists of one continuous variable and global constraints. Each state has a continuous cost attached to it, which is linear in the sojourn time, while a discrete cost is attached to each transition taken. We show the corresponding decision problem to be NP-complete and develop an FPTAS for finding an approximate solution. We have implemented a small prototype to compare the performance of these approximate and precise algorithms for this problem. Our results indicate that the proposed approximation schemes scale. Furthermore, we show that the same problem with infinite time horizon is in LOGSPACE.","PeriodicalId":347020,"journal":{"name":"2016 23rd International Symposium on Temporal Representation and Reasoning (TIME)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2016-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2016 23rd International Symposium on Temporal Representation and Reasoning (TIME)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/TIME.2016.9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
This paper studies optimal time-bounded control in a simple subclass of linear hybrid systems, which consists of one continuous variable and global constraints. Each state has a continuous cost attached to it, which is linear in the sojourn time, while a discrete cost is attached to each transition taken. We show the corresponding decision problem to be NP-complete and develop an FPTAS for finding an approximate solution. We have implemented a small prototype to compare the performance of these approximate and precise algorithms for this problem. Our results indicate that the proposed approximation schemes scale. Furthermore, we show that the same problem with infinite time horizon is in LOGSPACE.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
