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Kreim, H., Kugelmann, B., Pesch, H.J., and Breitner, M.H., Minimizing the Maximum Heating of a Re-Entering Space Shuttle: An Optimal Control Problem with Multiple Control Constraints, Optimal Control Applications and Methods, Vol.17, No. 1, pp. 45-69, 1996.

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Synthesis of Recursive Symbolic Models for Articulated.. - Hardt, Kreutz-Delgado (1998)   (Correct)

....of good symbolic manipulation packages, the effort necessary to generate these equations was greatly reduced. Thus, in recent years, powerful multiple shooting algorithms have been used with greater frequency to solve optimal control problems in the context of multipoint boundary value problems [23], 9] 30] Indirect methods have several advantages over their direct method cousins, one being simply that they converge much faster to a solution when they do converge which can be useful when many trajectories throughout the state space need to be calculated. Second, the class of problems ....

....notation and expanded to include gravitational terms, are newly presented for the purpose of calculating the adjoint equations in a two point boundary value problem. This system of equations may be used with a boundary value problem solver to solve the nonlinear H 2 and H1 control problems [9] [23], 30] 31 XII. Appendix We present here a list of identities that the spatial operators satisfy without proof. For derivations of these results see [14] 15] 37] Identity 10: Spatial operator identities. a) OEE OE = E OE OE = OE Gamma I = OE, b) OE Gamma1 = I Gamma E OE (c) E ....

H. Kreim, B. Kugelmann, H.J. Pesch, and M.H. Breitner, "Minimizing the Maximum Heating of a Re-entering Space Shuttle: An Optimal Control with Multiple Control Constraints," in Optimal Control Applications and Methods, Vol. 17, pp. 45-69, 1996.


Numerical Solution of Nonlinear ... Control Problems.. - Hardt, Helton.. (1997)   (Correct)

....0.60 Figure 7: A contour plot of the minimum values of Psi attained along closed loop system trajectories initialized at different ( Phi; Psi) and at R = 0:12 in the state space. 4. Acknowledgements A variation of the computational scheme proposed has already been used on aerospace problems [1, 6] in the context of differential games. We are grateful to O. von Stryk for describing his work on robots, as well as providing us with his program. We also express our appreciation to P. Hiltmann and P. Gill for the use of their programs. Many thanks to M. Breitner, M. Krsti c, D. Mayne, R.M. ....

H. Kreim, B. Kugelmann, H.J. Pesch, and M.H. Breitner, "Minimizing the maximum heating of a reentering space shuttle: an optimal control problem with multiple control constraints," Optimal Control Applications & Methods, 17(1), pp. 45-69, 1996.


Numerical Solution of Nonlinear ... Control Problems.. - Hardt, Helton..   (Correct)

.... = 0.60 Figure 7: A contour plot of the minimum values of Psi attained along closed loop system trajectories initialized at different ( Phi; Psi) and at R = 0:12 in the state space. 4. Acknowledgements A variation of the computational scheme proposed has already been used on aerospace problems [1, 6] in the context of differential games. We are grateful to O. von Stryk for describing his work on robots, as well as providing us with his program. We also express our appreciation to P. Hiltmann and P. Gill for the use of their programs. Many thanks to M. Breitner, M. Krsti c, D. Mayne, R.M. ....

H. Kreim, B. Kugelmann, H.J. Pesch, and M.H. Breitner, "Minimizing the maximum heating of a reentering space shuttle: an optimal control problem with multiple control constraints," Optimal Control Applications & Methods, 17(1), pp. 45-69, 1996.


Numerical Solution of Nonlinear ... Control Problems.. - Hardt, Helton..   (Correct)

....controller is constructed which satisfies these constraints. Graphical contour plots highlight the system performance and transient behavior one can predict given our model. VIII. Acknowledgements A variation of the computational scheme proposed has already been used on aerospace problems [7] [14] in the context of differential games. We are grateful to O. von Stryk for describing his work on robots, as well as providing us with his program. We also express our appreciation to P. Hiltmann and P. Gill for the use of their programs. Many thanks to M. Breitner, M. Krsti c, D. Mayne, R.M. ....

H. Kreim, B. Kugelmann, H.J. Pesch, and M.H. Breitner, "Minimizing the maximum heating of a re-entering space shuttle: an optimal control problem with multiple control constraints," Optimal Control Applications & Methods, 17(1), pp. 45-69, 1996.


Optimal Control and Flight Trajectory Optimization Applied to.. - Ranta (2004)   (Correct)

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Kreim, H., Kugelmann, B., Pesch, H.J., and Breitner, M.H., Minimizing the Maximum Heating of a Re-Entering Space Shuttle: An Optimal Control Problem with Multiple Control Constraints, Optimal Control Applications and Methods, Vol.17, No. 1, pp. 45-69, 1996.

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