{"title":"The Restricted Newton Method for Fast Nonlinear Model Predictive Control","authors":"A. Maitland, C. Jin, J. McPhee","doi":"10.1115/dscc2019-9067","DOIUrl":null,"url":null,"abstract":"\n We introduce the Restricted Newton’s Method (RNM), a basic optimization method, to accelerate model predictive control turnaround times. RNM is a hybrid of Newton’s method (NM) and gradient descent (GD) that can be used as a building block in nonlinear programming. The two parameters of RNM are the subspace on which we restrict the Newton steps and the maximal size of the GD step. We present a convergence analysis of RNM and demonstrate how these parameters can be selected for MPC applications using simple machine learning methods. This leads to two parameter selection strategies with different convergence behaviour. Lastly, we demonstrate the utility of RNM on a sample autonomous vehicle problem with promising results.","PeriodicalId":41412,"journal":{"name":"Mechatronic Systems and Control","volume":"111 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2019-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mechatronic Systems and Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1115/dscc2019-9067","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 1
Abstract
We introduce the Restricted Newton’s Method (RNM), a basic optimization method, to accelerate model predictive control turnaround times. RNM is a hybrid of Newton’s method (NM) and gradient descent (GD) that can be used as a building block in nonlinear programming. The two parameters of RNM are the subspace on which we restrict the Newton steps and the maximal size of the GD step. We present a convergence analysis of RNM and demonstrate how these parameters can be selected for MPC applications using simple machine learning methods. This leads to two parameter selection strategies with different convergence behaviour. Lastly, we demonstrate the utility of RNM on a sample autonomous vehicle problem with promising results.
期刊介绍：
This international journal publishes both theoretical and application-oriented papers on various aspects of mechatronic systems, modelling, design, conventional and intelligent control, and intelligent systems. Application areas of mechatronics may include robotics, transportation, energy systems, manufacturing, sensors, actuators, and automation. Techniques of artificial intelligence may include soft computing (fuzzy logic, neural networks, genetic algorithms/evolutionary computing, probabilistic methods, etc.). Techniques may cover frequency and time domains, linear and nonlinear systems, and deterministic and stochastic processes. Hybrid techniques of mechatronics that combine conventional and intelligent methods are also included. First published in 1972, this journal originated with an emphasis on conventional control systems and computer-based applications. Subsequently, with rapid advances in the field and in view of the widespread interest and application of soft computing in control systems, this latter aspect was integrated into the journal. Now the area of mechatronics is included as the main focus. A unique feature of the journal is its pioneering role in bridging the gap between conventional systems and intelligent systems, with an equal emphasis on theory and practical applications, including system modelling, design and instrumentation. It appears four times per year.
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