Constraint Splitting and Projection Methods for Optimal Control of Double Integrator

Heinz H. Bauschke (), Regina S. Burachik () and C. Yalçın Kaya ()
Additional contact information
Heinz H. Bauschke: University of British Columbia, Department of Mathematics
Regina S. Burachik: University of South Australia, School of IT & Mathematical Sciences
C. Yalçın Kaya: University of South Australia, School of Information Technology and Mathematical Sciences

Chapter Chapter 2 in Splitting Algorithms, Modern Operator Theory, and Applications, 2019, pp 45-68 from Springer

Abstract: Abstract We consider the minimum-energy control of a car, which is modelled as a point mass sliding on the ground in a fixed direction, and so it can be mathematically described as the double integrator. The control variable, representing the acceleration or the deceleration, is constrained by simple bounds from above and below. Despite the simplicity of the problem, it is not possible to find an analytical solution to it because of the constrained control variable. To find a numerical solution to this problem we apply three different projection-type methods: (i) Dykstra’s algorithm, (ii) the Douglas–Rachford (DR) method and (iii) the Aragón Artacho–Campoy (AAC) algorithm. To the knowledge of the authors, these kinds of (projection) methods have not previously been applied to continuous-time optimal control problems, which are infinite-dimensional optimization problems. The problem we study in this article is posed in infinite-dimensional Hilbert spaces. Behaviour of the DR and AAC algorithms are explored via numerical experiments with respect to their parameters. An error analysis is also carried out numerically for a particular instance of the problem for each of the algorithms.

Keywords: Optimal control; Dykstra projection method; Douglas-Rachford method; Aragón Artacho–Campoy algorithm; Linear quadratic optimal control; Control constraints; Numerical methods; 49M27; 65K10; 90C20 (search for similar items in EconPapers)
Date: 2019
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-25939-6_2

Ordering information: This item can be ordered from
http://www.springer.com/9783030259396

DOI: 10.1007/978-3-030-25939-6_2

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().