Some comments on DAE theory for IRK methods and trajectory optimization

DOI10.1016/S0377-0427(00)00306-XzbMath0956.65070WikidataQ126459420 ScholiaQ126459420MaRDI QIDQ1578851

Neil Biehn, Tracey Westbrook, Stephen L. Campbell, Laurent O. Jay

Publication date: 4 September 2000

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

zbMATH Keywords

implicit Runge-Kutta methodindexdifferential algebraic equationtrajectory optimizationorder reductionindustrial package SOCS

Mathematics Subject Classification ID

Implicit ordinary differential equations, differential-algebraic equations (34A09) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical methods for differential-algebraic equations (65L80)

Related Items

A Survey on Optimal Control Problems with Differential-Algebraic Equations, A full-space quasi-Lagrange-Newton-Krylov algorithm for trajectory optimization problems, Direct transcription solution of high index optimal control problems and regular Euler-Lagrange equations, Review of formulations for structural and mechanical system optimization, Global error estimates for a uniparametric family of stiffly accurate Runge-Kutta collocation methods on singularly perturbed problems, The Flexibility of DAE Formulations, Compensating for order variation in mesh refinement for direct transcription methods, On the global error of special Runge-Kutta methods applied to linear differential algebraic equations, Compensating for order variation in mesh refinement for direct transcription methods. II: Computational experience

Uses Software

• RODAS
• SOCS

Cites Work

• Error of Rosenbrock methods for stiff problems studied via differential algebraic equations
• A new approach to Lipschitz continuity in state constrained optimal control
• Collocation methods for differential-algebraic equations of index 3
• A sparse nonlinear optimization algorithm
• Orbit bifurcations and quantum fluctuation statistics
• Convergence of Runge-Kutta methods for differential-algebraic systems of index 3
• Convergence of a class of Runge-Kutta methods for differential-algebraic systems of index 2
• Error Estimates for a Discrete Approximation to Constrained Control Problems
• Discrete approximations to optimal trajectories using direct transcription and nonlinear programming
• The method of orienting curves and its application to manipulator trajectory planning
• Extremal solutions of some constrained control problems^∗
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