{"title":"利用有偏核密度估计求解机会约束最优控制问题的热启动方法","authors":"Rachel E. Keil, Mrinal Kumar, Anil V. Rao","doi":"10.1115/1.4052173","DOIUrl":null,"url":null,"abstract":"A warm start method is developed for efficiently solving complex chance constrained optimal control problems using biased kernel density estimators and Legendre–Gauss–Radau collocation. To address the computational challenges, the warm start method improves both the starting point for the chance constrained optimal control problem, as well as the efficiency of cycling through mesh refinement iterations. The improvement is accomplished by tuning a parameter of the kernel density estimator, as well as implementing a kernel switch as part of the solution process. Additionally, the number of samples for the biased kernel density estimator is set to incrementally increase through a series of mesh refinement iterations. Thus, the warm start method is a combination of tuning a parameter, a kernel switch, and an incremental increase in sample size. This warm start method is successfully applied to solve two challenging chance constrained optimal control problems in a computationally efficient manner using biased kernel density estimators and Legendre–Gauss–Radau collocation. [DOI: 10.1115/1.4052173]","PeriodicalId":54846,"journal":{"name":"Journal of Dynamic Systems Measurement and Control-Transactions of the Asme","volume":"50 1","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2021-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Warm Start Method for Solving Chance Constrained Optimal Control Problems Using Biased Kernel Density Estimators\",\"authors\":\"Rachel E. Keil, Mrinal Kumar, Anil V. Rao\",\"doi\":\"10.1115/1.4052173\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A warm start method is developed for efficiently solving complex chance constrained optimal control problems using biased kernel density estimators and Legendre–Gauss–Radau collocation. To address the computational challenges, the warm start method improves both the starting point for the chance constrained optimal control problem, as well as the efficiency of cycling through mesh refinement iterations. The improvement is accomplished by tuning a parameter of the kernel density estimator, as well as implementing a kernel switch as part of the solution process. Additionally, the number of samples for the biased kernel density estimator is set to incrementally increase through a series of mesh refinement iterations. Thus, the warm start method is a combination of tuning a parameter, a kernel switch, and an incremental increase in sample size. This warm start method is successfully applied to solve two challenging chance constrained optimal control problems in a computationally efficient manner using biased kernel density estimators and Legendre–Gauss–Radau collocation. [DOI: 10.1115/1.4052173]\",\"PeriodicalId\":54846,\"journal\":{\"name\":\"Journal of Dynamic Systems Measurement and Control-Transactions of the Asme\",\"volume\":\"50 1\",\"pages\":\"\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2021-08-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Dynamic Systems Measurement and Control-Transactions of the Asme\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1115/1.4052173\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Dynamic Systems Measurement and Control-Transactions of the Asme","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1115/1.4052173","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
Warm Start Method for Solving Chance Constrained Optimal Control Problems Using Biased Kernel Density Estimators
A warm start method is developed for efficiently solving complex chance constrained optimal control problems using biased kernel density estimators and Legendre–Gauss–Radau collocation. To address the computational challenges, the warm start method improves both the starting point for the chance constrained optimal control problem, as well as the efficiency of cycling through mesh refinement iterations. The improvement is accomplished by tuning a parameter of the kernel density estimator, as well as implementing a kernel switch as part of the solution process. Additionally, the number of samples for the biased kernel density estimator is set to incrementally increase through a series of mesh refinement iterations. Thus, the warm start method is a combination of tuning a parameter, a kernel switch, and an incremental increase in sample size. This warm start method is successfully applied to solve two challenging chance constrained optimal control problems in a computationally efficient manner using biased kernel density estimators and Legendre–Gauss–Radau collocation. [DOI: 10.1115/1.4052173]
期刊介绍:
The Journal of Dynamic Systems, Measurement, and Control publishes theoretical and applied original papers in the traditional areas implied by its name, as well as papers in interdisciplinary areas. Theoretical papers should present new theoretical developments and knowledge for controls of dynamical systems together with clear engineering motivation for the new theory. New theory or results that are only of mathematical interest without a clear engineering motivation or have a cursory relevance only are discouraged. "Application" is understood to include modeling, simulation of realistic systems, and corroboration of theory with emphasis on demonstrated practicality.