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The role of symplectic integrators in optimal control

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Published in Optimal Control Applications and Methods. 2009, vol. 30, no. 4, p. 367-382
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 integratorBackward error analysisSub-Riemannian geometryMartinetAbnormal geodesicOrbital transferSubmerged rigid body
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CHYBA, Monique, HAIRER, Ernst, VILMART, Gilles. The role of symplectic integrators in optimal control. In: Optimal Control Applications and Methods, 2009, vol. 30, n° 4, p. 367-382. https://archive-ouverte.unige.ch/unige:5210

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Deposited on : 2010-02-16

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