×

Second-variation methods in dynamic optimization. (English) Zbl 0172.13103


PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Longmuir, A. G.,Numerical Computation of Quasi-Optimal Feedback Control Laws and Optimal Control Programs, The University of British Columbia, Ph. D. Thesis, 1968.
[2] Merriam, C. W.,An Algorithm for the Iterative Solution of a Class of Two-Point Boundary Value Problems, SIAM Journal on Control, Vol. 2, No. 1, 1964. · Zbl 0146.13902
[3] Breakwell, J. V., Speyer, J. L., andBryson, A. E.,Optimization and Control of Nonlinear Systems Using the Second Variation, SIAM Journal on Control, Vol. 1, No. 2, 1963. · Zbl 0135.32901
[4] McReynolds, S. R., andBryson, A. E.,A Successive Sweep Method for Solving Optimal Programming Problems, Proceedings of the 1965 Joint Automatic Control Conference, Troy, New York. · Zbl 0183.17102
[5] McGill, R., andKenneth, P.,Solution of Variational Problems by Means of a Generalized Newton-Raphson Operator, AIAA Journal, Vol. 2, No. 10, 1964. · Zbl 0133.38803
[6] Keley, H. J., Kopp, R. E., andMoyer, H. G.,A Trajectory Optimization Technique Based Upon the Theory of the Second Variation, Celestial Mechanics and Astrodynamics, Edited by V. G. Szebehely, Academic Press, New York, 1964.
[7] Kelley, H. J.,Method of Gradients, Optimization Techniques, Edited by G. Leitmann, Academic Press, New York, 1962.
[8] Bryson, A. E., andDenham, W. F.,A Steepest-Ascent Method for Solving Optimal Programming Problems, Journal of Applied Mechanics, Vol. 84, No. 2, 1962. · Zbl 0112.20003
[9] Sutherland, J. W., andBohn, E. V.,A Numerical Trajectory Optimization Method Suitable for a Computer of Limited Memory, IEEE Transactions on Automatic Control, Vol. AC-11, No. 3, 1966.
[10] Kenneth, P., andMcGill, R.,Two-Point Boundary-Value Problem Techniques, Advances in Control Systems, Vol. 3, Edited by C. T. Leondes, Academic Press, New York, 1966. · Zbl 0171.36502
[11] Kalaba, R. E.,On Nonlinear Differential Equations, the Maximum Operation, and Monotone Convergence, Journal of Mathematics and Mechanics, Vol. 8, No. 4, 1959. · Zbl 0092.07703
[12] Gelfand, I. M., andFomin, S. V.,Calculus of Variations, Prentice-Hall, Englewood Cliffs, New Jersey, 1963.
[13] Tapley, B. D., andLewallen, J. M.,Comparison of Several Numerical Optimization Methods, Journal of Optimization Theory and Applications, Vol. 1, No. 1, 1967. · Zbl 0149.42502
[14] Schley, C. H., Jr., andLee, I.,Optimal Control Computation by the Newton-Raphson Method and the Riccati Transformation, IEEE Transactions on Automatic Control, Vol. AC-12, No. 2, 1967.
[15] Dreyfus, S. E.,Control Problems with Linear Dynamics, Quadratic Criterion, and Linear Terminal Constraints, IEEE Transactions on Automatic Control, Vol. AC-12, No. 3, 1967.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.