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Sequential gradient-restoration algorithm for optimal control problems. (English) Zbl 0192.51802


Keywords:

control theory
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[1] Miele, A.,Gradient Methods in Control Theory, Part 1, Ordinary Gradient Method, Rice University, Aero-Astronautics Report No. 60, 1969. · Zbl 0194.46402
[2] Miele, A., andPritchard, R. E.,Gradient Methods in Control Theory, Part 2, Sequential Gradient-Restoration Algorithm, Rice University, Aero-Astronautics Report No. 62, 1969. · Zbl 0194.46501
[3] Damoulakis, J. N.,Gradient Methods in Control Theory, Part 3, Sequential Gradient-Restoration Algorithm: Numerical Examples, Rice University, Aero-Astronautics Report No. 65, 1969. · Zbl 0194.46502
[4] Damoulakis, J. N.,Gradient Methods in Control Theory, Part 4, Sequential Gradient-Restoration Algorithm: Further Numerical Examples, Rice University, Aero-Astronautics Report No. 67, 1970. · Zbl 0195.44202
[5] Damoulakis, J. N.,Gradient Methods in Control Theory, Part 5, Sequential Gradient-Restoration Algorithm: Additional Numerical Examples, Rice University, Aero-Astronautics Report No. 73, 1970. · Zbl 0195.44203
[6] Bryson, A. E., andDenham, W. F.,A Steepest-Ascent Method for Solving Optimum Programming Problems, Journal of Applied Mechanics, Vol. 84, No. 2, 1962. · Zbl 0112.20003
[7] Kelley, H. J.,Gradient Theory of Optimal Flight Paths, ARS Journal, Vol. 30, No. 10, 1960. · Zbl 0096.42002
[8] Miele, A., Heideman, J. C., andDamoulakis, J. N.,The Restoration of Constraints in Holonomic and Nonholonomic Problems, Journal of Optimization Theory and Applications, Vol. 3, No. 5, 1969. · Zbl 0172.13001
[9] Long, R. S.,Newton-Raphson Operator; Problems with Undetermined End Points, AIAA Journal, Vol. 3, No. 7, 1965.
[10] Miele,Method of Particular Solutions for Linear, Two-Point Boundary-Value Problems, Journal of Optimization Theory and Applications, Vol. 2, No. 4, 1968. · Zbl 0176.04901
[11] Heideman, J. C.,Use of the Method of Particular Solutions in Nonlinear, Two-Point Boundary-Value Problems, Journal of Optimization Theory and Applications, Vol. 2, No. 6, 1968. · Zbl 0177.35604
[12] Miele, A., andIyer, R.,General Technique for Solving Nonlinear, Two-Point Boundary-Value Problems via the Method of Particular Solutions, Rice University, Aero-Astronautics Report No. 63, 1969. · Zbl 0208.41802
[13] Miele, A., Editor,Theory of Optimum Aerodynamic Shapes, Academic Press, New York, 1965. · Zbl 0265.76076
[14] Hestenes, M. R.,Multiplier and Gradient Methods, Journal of Optimization Theory and Applications, Vol. 4, No. 5, 1969.
[15] Ralston, A.,Numerical Integration Methods for the Solution of Ordinary Differential Equations, Mathematical Methods for Digital Computers, Vol. 1, Edited by A. Ralston and H. S. Wilf, John Wiley and Sons, New York, 1960.
[16] Lasdon, L. S., Mitter, S. K., andWaren, A. D.,The Conjugate Gradient Method for Optimal Control Problems, IEEE Transactions on Automatic Control, Vol. AC-12, No. 2, 1967.
[17] Hestenes, M. R.,Calculus of Variations and Optimal Control Theory, McGraw-Hill Book Company, New York, 1967. · Zbl 0173.35703
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