Symplectic adaptive algorithm for solving nonlinear two-point boundary value problems in astrodynamics

DOI10.1007/s10569-011-9360-4zbMath1270.70074OpenAlexW2029874783MaRDI QIDQ362703

Mohammad Hasan, M. Dambrine

Publication date: 30 August 2013

Published in: Celestial Mechanics and Dynamical Astronomy (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10569-011-9360-4

zbMATH Keywords

two-point boundary value problemnonlinear optimal controlhalo orbitsastrodynamicsadaptive symplectic algorithmdual variational principle

Mathematics Subject Classification ID

Computational methods for problems pertaining to mechanics of particles and systems (70-08) Control of mechanical systems (70Q05) Orbital mechanics (70M20) Control/observation systems governed by ordinary differential equations (93C15) Numerical methods for Hamiltonian systems including symplectic integrators (65P10)

Related Items (10)

A symplectic sequence iteration approach for nonlinear optimal control problems with state-control constraints ⋮ Energy-conserving methods for Hamiltonian boundary value problems and applications in astrodynamics ⋮ Numerical solution of some initial optimal control problems using the reproducing kernel Hilbert space technique ⋮ An \(hp\) symplectic pseudospectral method for nonlinear optimal control ⋮ Time-optimal reorientation of the rigid spacecraft using a pseudospectral method integrated homotopic approach ⋮ A composite pseudospectral method for optimal control problems with piecewise smooth solutions ⋮ Mathematical analysis of a human papillomavirus transmission model with vaccination and screening ⋮ A nonsmooth contact dynamic algorithm based on the symplectic method for multibody system analysis with unilateral constraints ⋮ A symplectic pseudospectral method for constrained time-delayed optimal control problems and its application to biological control problems ⋮ Multi-objective transfer to libration-point orbits via the mixed low-thrust and invariant-manifold approach

Cites Work

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• Application of high order expansions of two-point boundary value problems to astrodynamics
• Convergence rates for direct transcription of optimal control problems using collocation at Radau points
• A sixth-order accurate scheme for solving two-point boundary value problems in astrodynamics
• Determination of optimal feedback terminal controllers for general boundary conditions using generating functions
• Survey of Numerical Methods for Trajectory Optimization
• Analytic construction of periodic orbits about the collinear points
• Weak Hamiltonian finite element method for optimal control problems

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