Back to Search
Start Over
A numerical investigation of Brockett’s ensemble optimal control problems
- Source :
- Numerische Mathematik. 149:1-42
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- This paper is devoted to the numerical analysis of non-smooth ensemble optimal control problems governed by the Liouville (continuity) equation that have been originally proposed by R.W. Brockett with the purpose of determining an efficient and robust control strategy for dynamical systems. A numerical methodology for solving these problems is presented that is based on a non-smooth Lagrange optimization framework where the optimal controls are characterized as solutions to the related optimality systems. For this purpose, approximation and solution schemes are developed and analysed. Specifically, for the approximation of the Liouville model and its optimization adjoint, a combination of a Kurganov–Tadmor method, a Runge–Kutta scheme, and a Strang splitting method are discussed. The resulting optimality system is solved by a projected semi-smooth Krylov–Newton method. Results of numerical experiments are presented that successfully validate the proposed framework.
- Subjects :
- msc:49K20
Scheme (programming language)
Dynamical systems theory
Applied Mathematics
Numerical analysis
MathematicsofComputing_NUMERICALANALYSIS
msc:35L03
Optimal control
Numerical methodology
Computational Mathematics
symbols.namesake
Strang splitting
Lagrange multiplier
ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION
symbols
msc:49M15
Applied mathematics
msc:65M08
ddc:510
Robust control
computer
Mathematics
computer.programming_language
Subjects
Details
- ISSN :
- 09453245 and 0029599X
- Volume :
- 149
- Database :
- OpenAIRE
- Journal :
- Numerische Mathematik
- Accession number :
- edsair.doi.dedup.....5c7733b8784255de67915d5851eefc60