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Constraint Splitting and Projection Methods for Optimal Control of Double Integrator

In: Splitting Algorithms, Modern Operator Theory, and Applications

Author

Listed:
  • 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)

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.

Suggested Citation

  • Heinz H. Bauschke & Regina S. Burachik & C. Yalçın Kaya, 2019. "Constraint Splitting and Projection Methods for Optimal Control of Double Integrator," Springer Books, in: Heinz H. Bauschke & Regina S. Burachik & D. Russell Luke (ed.), Splitting Algorithms, Modern Operator Theory, and Applications, chapter 0, pages 45-68, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-25939-6_2
    DOI: 10.1007/978-3-030-25939-6_2
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