A Sweeping Gradient Method for Ordinary Differential Equations with Events

Benjamin W. L. Margolis ()
Additional contact information
Benjamin W. L. Margolis: NASA Ames Research Center

Journal of Optimization Theory and Applications, 2023, vol. 199, issue 2, No 7, 600-638

Abstract: Abstract In this paper, we use the calculus of variations to derive a sensitivity analysis for ordinary differential equations with events. This sweeping gradient method (SGM) requires a forward sweep to evaluate the original model and a backwards sweep of the adjoint to compute the sensitivity. The method is applied to canonical optimal control problems with numerical examples, including the sampled linear quadratic regulator and the optimal time-switching and state-switching for minimum-time transfer of the double integrator. We show that the application of the SGM for these examples matches the gradient determined analytically. Numerical examples are produced using gradient-based optimization algorithms. The emphasis of this work is on modeling considerations for the effective application of this method.

Keywords: Variational derivative; Ordinary differential equations with events; Parameter optimization; Adjoint; Sweeping method; LQR; Switching schedule; 49M05; 90C31; 65K10; 34H05 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-023-02303-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:joptap:v:199:y:2023:i:2:d:10.1007_s10957-023-02303-3

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-023-02303-3

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().