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Scientific article
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English

The role of symplectic integrators in optimal control

Published inOptimal control applications & methods, vol. 30, no. 4, p. 367-382
Publication date2009
Abstract

For general optimal control problems, Pontryagin's maximum principle gives necessary optimality conditions which are in the form of a Hamiltonian differential equation. For its numerical integration, symplectic methods are a natural choice. This article investigates to which extent the excellent performance of symplectic integrators for long-time integrations in astronomy and molecular dynamics carries over to problems in optimal control. Numerical experiments supported by a backward error analysis show that, for problems in low dimension close to a critical value of the Hamiltonian, symplectic integrators have a clear advantage. This is illustrated at the Martinet case in sub-Riemannian geometry. For problems like the orbital transfer of a spacecraft or the control of a submerged rigid body such an advantage cannot be observed. The Hamiltonian system is a boundary value problem and the time interval is in general not large enough so that symplectic integrators could benefit from their structure preservation of the flow.

Keywords
  • Symplectic integrator
  • Backward error analysis
  • Sub-Riemannian geometry
  • Martinet
  • Abnormal geodesic
  • Orbital transfer
  • Submerged rigid body
Citation (ISO format)
CHYBA, Monique, HAIRER, Ernst, VILMART, Gilles. The role of symplectic integrators in optimal control. In: Optimal control applications & methods, 2009, vol. 30, n° 4, p. 367–382. doi: 10.1002/oca.855
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Article (Accepted version)
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Identifiers
ISSN of the journal0143-2087
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