Compensating for order variation in mesh refinement for direct transcription methods

DOI10.1016/S0377-0427(00)00465-9zbMath0971.65075MaRDI QIDQ1841951

Neil Biehn, John T. Betts, William P. Huffman, Stephen L. Campbell

Publication date: 26 October 2001

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

algorithmsoptimal controlnumerical exampleimplicit Runge-Kutta methoddifferential algebraic equationmesh refinementorder reductiondirect transcription

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Implicit ordinary differential equations, differential-algebraic equations (34A09) Linear ordinary differential equations and systems (34A30) Existence theories for optimal control problems involving ordinary differential equations (49J15) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical methods for differential-algebraic equations (65L80) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items

Direct transcription solution of high index optimal control problems and regular Euler-Lagrange equations ⋮ A novel mesh discretization strategy for numerical solution of optimal control problems in aerospace engineering ⋮ Review of formulations for structural and mechanical system optimization ⋮ Solving optimal control problems with control delays using direct transcription ⋮ Adaptive mesh refinement method for solving optimal control problems using interpolation error analysis and improved data compression ⋮ Examination of solving optimal control problems with delays using GPOPS-II ⋮ Direct transcription solution of optimal control problems with higher-order state constraints: theory vs practice ⋮ Adaptive time-mesh refinement in optimal control problems with state constraints ⋮ Compensating for order variation in mesh refinement for direct transcription methods. II: Computational experience

Uses Software

• SOCS
• OTIS

Cites Work

• A sparse nonlinear optimization algorithm
• Some comments on DAE theory for IRK methods and trajectory optimization
• Convergence of a class of Runge-Kutta methods for differential-algebraic systems of index 2
• Direct trajectory optimization using nonlinear programming and collocation
• Application of sparse nonlinear programming to trajectory optimization
• Path-constrained trajectory optimization using sparse sequential quadratic programming
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