Legendre Approximation for Solving a Class of Nonlinear Optimal Control Problems

Show more

References

[1] R. R. Bless, D. H. Hoges and H. Seywald, “Finite Element Method for the Solution of State-Constrained Optimal Control Problems,” Journal of Guidance, Control, and Dynamics, Vol. 18, No. 5, 1995, pp. 1036-1043.
doi:10.2514/3.21502

[2] R. Bulrisch and D. Kraft, “Compu-tational Optimal Control,” Birkhauser, Boston, 1994.

[3] G. Elnagar, M. A. Kazemi and M. Razzaghi, “The Pseudospectral Legendre Method for Discretizing Optimal Control Problems,” IEEE Transactions on Automatic Con- trol, Vol. 40, No. 10, 1995, pp. 1793-1796.
doi:10.1109/9.467672

[4] G. N. Elnagar and M. A. Kazemi, “Pseudospectral Chebyshev Optimal Control of Constrained Nonlinear Dynamical Systems,” Computational Optimization and Applications, Vol. 11, No. 2, 1998, pp. 195-217.
doi:10.1109/9.467672

[5] W. W. Hager, “Multiplier Methods for Nonlinear Optimal Control Problems,” SIAM Journal on Numerical Anal, Vol. 27, No. 4, 1990, pp. 1061-1080.
doi:10.1137/0727063

[6] A. L. Herman and B. A. Conway, “Direct Trajectory Optimization Using Collocation Based on High-Order Gauss-Lobatoo Quadrature Rules,” Journal of Guidance, Control, and Dynamics, and Dynamics, Vol. 19, No. 3, 1996, pp. 592-599. doi:10.2514/3.21662

[7] M. Ross and F. Fahroo, “Legendre Pseudospectral Approximations of Optimal Control Problems,” Lecture Notes in Control and Information Sciences, Vol. 295, No. 1, 2003, pp. 327-342.

[8] J. Vlassen-broeck and R. V. Dooren, “A Chebyshev Technique for Solving Nonlinear Optimal Control Problems,” IEEE Transactions on Automatic Control, Vol. 33, No. 4, 1988, pp. 333-340. 10.1109/9.192187

[9] H. Seywald and R. R. Kumar, “Finite Difference Scheme for Automatic Costate Calculation,” Journal of Guidance, Control, and Dynamics, and Dynamics, Vol. 19, No. 1, 1996, pp. 231-239. doi:10.2514/3.21603

[10] K. Schittkowskki, “NLPQL: A Fortran Subroutine for Solving Constrained Nonlinear Programming Problems,” Operations Research Annals, Vol. 5, No. 2, 1985, pp. 385-400.

[11] M. Razzaghi and G. Elnagar, “A Legendre Technique For Solving Time-Varing Linear Quadratic Optimal Control Problems,” Journal of the Franklin Institute, Vol. 330, No. 3, 1993, pp. 453-463.
doi:10.1016/0016-0032(93)90092-9

[12] O. V. Stryk, “Nu-merical Solution of Optimal Control Problems by Direct Col-location,” In: R. Bulrisch, A. Miele, J. Stoer and K. H. Well, Eds., Optional Control of Variations, Optimal Control Theory and Numerical Methods, International Series of Numerical Mathematics, Birkh?user Verlag, Basel, 1993, pp. 129-143.