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  4. Tutorial problems for nonsmooth dynamics and optimal control: ski jumping and accelerating a bike without pedaling
 
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Tutorial problems for nonsmooth dynamics and optimal control: ski jumping and accelerating a bike without pedaling

Publikationstyp
Journal Article
Date Issued
2024-12-23
Sprache
English
Author(s)
Golembiewski, Julian  
Regelungstechnik E-14  
Faulwasser, Timm  
Regelungstechnik E-14  
TORE-URI
https://tore.tuhh.de/handle/11420/52949
Journal
IEEE control systems letters  
Volume
8
Start Page
3291
End Page
3296
Citation
Control Systems Letters 8: 3291-3296 (2024)
Publisher DOI
10.1109/LCSYS.2024.3521556
Scopus ID
2-s2.0-85213533298
Publisher
IEEE
Nonsmooth phenomena, such as abrupt changes, impacts, and switching behaviors, frequently arise in real-world systems and present significant challenges for traditional optimal control methods, which typically assume smoothness and differentiability. These phenomena introduce numerical challenges in both simulation and optimization, highlighting the need for specialized solution methods. Although various applications and test problems have been documented in the literature, many are either overly simplified, excessively complex, or narrowly focused on specific domains. On this canvas, this paper proposes two novel tutorial problems that are both conceptually accessible and allow for further scaling of problem difficulty. The first problem features a simple ski jump model, characterized by state-dependent jumps and sliding motion on impact surfaces. This system does not involve control inputs and serves as a testbed for simulating nonsmooth dynamics. The second problem considers optimal control of a special type of bicycle model. This problem is inspired by practical techniques observed in BMX riding and mountain biking, where riders accelerate their bike without pedaling by strategically shifting their center of mass in response to the track's slope.
Subjects
hybrid systems | modeling | numerical algorithms | optimal control
DDC Class
600: Technology
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