Some comments on DAE theory for IRK methods and trajectory optimization

Journal of Computational and Applied Mathematics

Volumn 120, Issue 1, 2000, Pages 109-131

  Biehn, Neil ^a   Campbell, Stephen L ^a   Jay, Laurent ^b   Westbrook, Tracey ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

^b UNIVERSITY OF IOWA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; COMPUTATIONAL COMPLEXITY; CONSTRAINT THEORY; OPTIMAL CONTROL SYSTEMS; ORDINARY DIFFERENTIAL EQUATIONS; PROBLEM SOLVING; QUADRATIC PROGRAMMING; SOFTWARE ENGINEERING;

DIFFERENTIAL ALGEBRAIC EQUATION; IMPLICIT RUNGE-KUTTA METHOD; SEQUENTIAL QUADRATIC PROGRAMMING; SPARSE OPTIMAL CONTROL SOFTWARE; TRAJECTORY OPTIMIZATION PROBLEM;

RUNGE KUTTA METHODS;

EID: 0034250710     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(00)00306-X     Document Type: Article

References (24)

1. A. Barclay, P.E. Gill, J. Ben Rosen, SQP methods and their application to numerical optimal control, Report NA 97-3, Department of Mathematics, University of California, San Diego, 1997.
2. J.T. Betts P.D. Frank A sparse nonlinear optimization algorithm J. Optim. Theory Appl. 82 1994 519 541
3. J.T. Betts W.P. Huffman Mesh refinement in direct transcription methods for optimal control Optim. Control Appl. Methods 19 1998 1 21
4. L.T. Biegler Optimization strategies for complex process models Adv. Chem. Eng. 18 1992 197 256
5. H.G. Bock H.X. Phu J.P. Schlöder Extremal solutions of some constrained control problems Optimization 35 1995 345 355
6. H.G. Bock H.X. Phu J.P. Schlöder The method of orienting curves and its application to manipulator trajectory planning Numer. Funct. Anal. Optim. 18 1997 213 225
7. H.G. Bock, J.P. Schlöder, V.H. Schulz, Differential-algebraic equations and their connection to optimization, Heidelberg, preprint 96-58, 1996. Documentation for a SIAM short course.
8. K.E. Brenan Differential-algebraic equations issues in the direct transcription of path constrained optimal control problems Ann. Numer. Math. 1 1994 247 263
9. K.E. Brenan, A large-scale generalized reduced gradient algorithm for flight optimization and sizing problems, The Aerospace Corporation, ATR-94(8489)-3, 1994.
10. K.E. Brenan, S.L. Campbell, L.R. Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, SIAM, Philadelphia, PA, 1996.
11. S.L. Campbell High index differential algebraic equations Mech. Struct. Mach. 23 1995 199 222
12. J.E. Cuthrell L.T. Biegler On the optimization of differential-algebraic process systems A.I.Ch.E. J. 33 1987 1257 1270
13. A.L. Dontchev Error estimates for a discrete approximation to constrained control problems SIAM J. Numer. Anal. 18 1981 500 514
14. A.L. Dontchev W.W. Hager A new approach to Lipschitz continuity in state constrained optimal control Systems Control Lett. 35 1998 137 143
15. P.J. Enright, Optimal finite-thrust spacecraft trajectories using direct transcription and nonlinear programming, Ph.D. Thesis, University of Illinois, 1991.
16. P.J. Enright B.A. Conway Discrete approximations to optimal trajectories using direct transcription and nonlinear programming AIAA J. Guidance Control Dyn. 15 1992 994 1002
17. W.F. Feehery P.I. Barton Dynamic simulation and optimization with inequality path constraints Comp. Chem. Eng. 20 1996 S707 S712
18. E. Hairer L.O. Jay Implicit Runge–Kutta methods for higher index differential-algebraic systems WSSIAA, Contrib. Numer. Math. 2 1993 213 224
19. E. Hairer Ch. Lubich M. Roche The Numerical Solution of Differential-Algebraic Systems by Runge–Kutta Methods Lecture Notes in Mathematics Vol. 1409 1989 Springer Berlin
20. E. Hairer G. Wanner Solving Ordinary Differential Equations II, Stiff and Differential Algebraic Problems 2nd Revised Edition 1991 Springer Berlin
21. L.O. Jay Convergence of a class of Runge–Kutta methods for differential-algebraic systems of index 2 BIT 33 1993 137 150
22. L.O. Jay Collocation methods for differential-algebraic equations of index 3 Numer. Math. 65 1993 407 421
23. L.O. Jay, Runge–Kutta type methods for index three differential-algebraic equations with applications to Hamiltonian systems, Ph.D. Thesis, Department of Mathematics, University of Geneva, Switzerland, 1994.
24. L.O. Jay Convergence of a class of Runge–Kutta methods for differential-algebraic systems of index 3 Appl. Numer. Math. 17 1995 97 118