Optimal Control-1950 to 1985

IEEE Control Systems

Volumn 16, Issue 3, 1996, Pages 26-33

  Bryson, Arthur E ^a  

^a The Department of Aeronautics and Astronautics   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CONTROL THEORY; DYNAMIC PROGRAMMING; LINEAR PROGRAMMING; NONLINEAR PROGRAMMING; RANDOM PROCESSES; VARIATIONAL TECHNIQUES;

CLASSICAL CONTROL THEORY; H INFINITY CONTROL; WORST CASE CONTROL;

OPTIMAL CONTROL SYSTEMS;

EID: 0030170303     PISSN: 1066033X     EISSN: None     Source Type: Journal    
DOI: 10.1109/37.506395     Document Type: Article

References (77)

1. H.H. Goldstine, A History of the Calculus of Variations from the 17th through the 19th Century, Springer-Verlag, 1980.
2. O. Bolza. Vorlesungen uber Variationsrechnung, Leipzig u. Berlin. 1909.
3. G.H. Bliss, Lectures on the Calculus of Variations, University of Chicago. 1946.
4. M.R. Hestenes, Calculus of Variations and Optimal Control Theory. Wiley, New York. 1966.
5. E.J. McShane. “On Multipliers for Lagrange Problems.” Amer. J. Math., LXI, 809-818, 1939.
6. P. Cicala, An Engineering Approach to the Calculus of Variations. Levrotto and Bella, Torino, 1957.
7. D.F. Lawden, Optimal Trajectories for Space Navigation, Butterworths, London, 1963.
8. D. McRuer, I. Ashkenas, and D. Graham, Aircraft Dynamics and Automatic Control. Princeton. 1973.
9. G. Newton, L.A. Gould, and T.E. Kaiser, Analytical Design of Linear Feedback Controls, Wiley. 1957.
10. S.S.L. Chang, Synthesis of Optimal Control Systems, McGraw-Hill, 1961.
11. R.E. Kalman, “Contributions to the Theory of Optimal Control,” Bol. de Soc. Math. Mexicana, p. 102. 1960.
12. M. Athans, ed., Special Issue on Linear-Quadratic Problems, IEEE Trans. Auto. Ctrl., vol. 16, no. 6, 1971.
13. N. Wax, ed., Collected Papers on Noise and Stochastic Processes, Dover. New York, 1954.
14. R.E. Kalman and R. Bucy, “New Results in Linear Filtering and Prediction,” Trans. ASME, vol. 83D, p. 95, 1961.
15. N. Weiner. “The Interpolation and Smoothing of Stationary Time Series.” MIT. Cambridge, 1949.
16. T.F. Gunckel and G.F. Franklin, “A General Solution for Linear Sampled-Data Control Systems,” Trans. ASME, vol. 85D, p. 197, 1963.
17. P.D. Joseph and J.T. Tou, “On Linear Control Theory,” Trans. AIEE, 80-3, 18, 1961.
18. H.A. Simon. “Dynamic Programming Under Uncertainty with a Quadratic Criterion,” Econometrica, vol. 24, pp. 74-81, 1956.
19. J.H. Laning and R.H. Battin, Random Processes in Automatic Control, McGraw-Hill, New York, 1956.
20. R.H. Battin. Astronautical Guidance, McGraw-Hill, New York, 1964.
21. R.H. Battin, “Space Guidance Evolution,” Jour. Guidance, Control, and Dynamics, vol. 5, no. 2, pp. 97-110, 1982.
22. G. Dantzig, Linear Progamming and Extensions, Princeton, 1963.
23. H. Kuhn and A.W. Tucker, “Nonlinear Programming,” Second Berkeley Symposium of Mathematical Statistics and Probability. Univ. Calif., 1951.
24. P.E. Gill, W. Murray, and M.H. Wright, Practical Optimization, Academic Press, New York, 1991.
25. P.E. Gill, W. Murray, M.A. Saunders, and M.H. Wright, “User's Guide for NPSOL (Version 4.0): A FORTRAN Package for Nonlinear Programming,” Stanford Univ. Dept. of Operations Research, January 1986.
26. U.L. Ly, “A Design Algorithm for Robust Low-Order Controllers,” Stanford Univ. Dept. of Aero/Astro. Rpt. 536, Ph.D. thesis, November 1992.
27. C.R. Hargraves and S.W. Paris, “Direct Trajectory Optimization Using Nonlinear Programming and Collocation,” Jour. Guidance, Control and Dynamics. vol. 10, no. 4, 1987.
28. H. Seywald. “Trajectory Optimization Based on Differential Inclusion,” Jour. Guidance, Control and Dynamics, vol. 17, no. 3, pp. 480-487, 1994.
29. D.E. Knuth, Fundamental Algorithms: Vol. 1 of the Art of Computer Programming. Addison-Wesley, Reading. MA, 1968.
30. R. Bellman, Dynamic Programming. Princeton. 1957.
31. S.E. Dreyfus, Dynamic Programming and the Calculus of Variations. Academic Press, N.Y, 1966.
32. A.E. Bryson and Y.C. Ho. Applied Optimal Control. Blaisdell. 1969, rev. printing, Hemisphere, 1975.
33. P. Dyer and S.R. McReynolds, The Computation and Theory of Optimal Control, Academic Press. 1970.
34. D. Jacobson and D. Mayne, Differential Dynamic Programming, American Elsevier. New York, 1970.
35. I.M. Gelfand and S.V. Fomin, Calculus of Variations, transl. by R.A. Silverman, Prentice-Hall, 1963.
36. L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze, and E.F. Mishchenko, The Mathematical Theory of Optimal Processes, Moscow, 1961, translated by K. N. Trirogoff, edited by L.W. Neustadt, Interscience, N.Y., 1962.
37. A.M. Letov, “Analytical Synthesis of Regulators,” Automation and Telemechanics, vol. 21, 1960; also editor of Optimal Automatic Control Systems, Moscow, 1967.
38. W. Hohmann, Die Erreichbarkeit der Himmelskorper, Oldenbourg, Munich, 1925.
39. G. Leitmann, ed., Optimization Techniques, Academic Press, N.Y., 1962.
40. M. Athans and P.L. Falb, Optimal Control. McGraw-Hill, N.Y., 1966.
41. A.E. Bryson and S.E. Ross, “Optimum Rocket Trajectories with Aerodynamic Drag,” Jet Propulsion, July 1958.
42. J.V. Breakwell. “The Optimintion of Trajectories,” SIAM Jour, vol. 7, 1959.
43. D.E. Okhotsimkii and T.M. Eneev, “Some Variational Problems Connected with the Launching of Artificial Satellites of the Earth,” Jour. Brit. Interplanet. Soc., vol. 16, no. 5, 1958.
44. H.B. Keller, Numerical Methods for Two-Point Boundary-Value Problems, Blaisdell. 1968.
45. R. Bulirsch, “Dic Mchrzielmcthode,” Carl Cranz Gesellschaft, Oberpfaffcnhoven, 1971; reprint 1993, Dept. Mathematics, Munich University of Technology.
46. W. Grimm, E. Berger, and H.J. Oberle, “User's Manual of the BNDSCO Computer Program for Solving Constrained Optimal Control Problems,” Hamburg Univ., Germany, June 1984.
47. H.J. Oberle and W. Grimm, “BNDSCO-A Program for the Numerical Solution of Optimal Control Problems,” DLR Inter. Rpt. 515-89/22, Oberpfaffenhoven, 1989.
48. H.J. Kelley. “Gradlent Theory of Optimal Flight Paths.” Jour: Amer. Rocket Soc., vol. 30, 1960.
49. A.V. Balakrishnan, ed., Conference on Computing Methods on Optimization Problems. Academic Press, New York, 1964.
50. A.E. Bryson and W.F. Denham. “A Steepest Ascent Method for Solving Optimum Programming Problems,” ASME Jour. Appl. Mech., vol. 29, Series E, 1962.
51. A.E. Bryson. Lecture Notes on Dynamic Optimization, Stanford Univ. 1992.
52. A.E. Bryson, M.N. Desai, and W.E. Hoffman, “The Energy-State Approximation in Performance Estimation of Supersonic Aircraft,” Journal: Aircraft, vol. 6, no. 6, pp. 481-487, 1969.
53. F. Kaiser, “The Climb of Jet Propelled Aircraft, Part 1: Speed Along the Path in Optimum Climb,” Ministry of Supply (Gt. Brit.), RTP/TIB Translation no. GDC/15/14ST, 1944.
54. K.J. Lush, “A Review of the Problem of Choosing a Climb Technique with Proposals for a New Climb Technique for High Performance Aircraft,” Aero. Res. Council, RM no. 2557, 1951.
55. E.S. Rutowski, “Energy Approach to the General Aircraft Performance Problem,” Jour. Aerospace Sci., vol. 21, no. 3, 1954.
56. J.V. Breakwell, J. Speyer, and A.E. Bryson. “Optimization and Control of Nonlinear Systems Using the Second Variation.” SIAM Jour. Control, Ser. A, vol. 1, no. 2, pp. 193-223. 1963.
57. H.J. Kelley, R.E. Kopp, and G. Moyer, “A Trajectory Optimization Technique Based Upon the Theory of the Second Variation,” AIAA AStrodynamics Conf., Yale Univ., 1963.
58. A. Miele, ed., Theory of Optimum Aerodynamic Shapes, Academic Press, 1965.
59. E.J. Haug and J.S. Arora, Applied Optimal Design, Wiley, 1979.
60. F.A. Valentine, “The Problem of Lagrange with Differential Inequalities as Added Side Conditions,” Contributions to the Calculus of Variations 1933-37. Univ. of Chicago.
61. J.L. Speyer and A.E. Bryson, “Optimal Progamming Problems with a Bounded State Space,” AIAA Jour., vol. 6. 1968.
62. R.K. Mehra and R.E. Davis, “A Generalized Gradient Method for Optimal Control Problems with Inequality Constraints and Singular Arcs,” IEEE Trans., vol. AC-17, pp. 69-78, 1972.
63. D.J. Bell and D.H. Jacobson, Singular Optimal Control Problems, Academic Press, New York, 1975.
64. G. Meyer and L. Cicolani, “Application of Nonlinear System Inverses to Automatic Flight Control,” Theory and Applications of Optimal Control in Aerospace Systems, AGARDograph 251, 1981.
65. R.E. Kalman, “Optimal Control and the Calculus of Variations.” Ch. 16 of Mathematical Optimization Techniques, Bellman, ed., Univ. Calif. Press, 1963.
66. C. Caratheodory, Calculus of Variations and Partial Differential Equations of First Order, R. Dean (transl.), Holden-Day, 1967 (originally in German, 1935).
67. A.G.J. MacFarlane, “ An Eigenvector Solution of the Optimal Linear Regulator,” Jour. Electron. Control, vol. 14, pp. 643-54, 1963.
68. R.E. Kalman and T. Englar, “The Automatic Synthesis Program,” NASA Contractor Report CR-475, 1966.
69. J.H. Wilkinson, R.S. Martin, and G. Peters, “The QR Algorithm for Real Hessenberg Matrices.” Numer. Mat., vol. 14, pp. 219-231, 1970.
70. J.G.P. Francis, “The QR Transformation. Parts I and II,” Comput. J., vol. 4, pp. 265-271. 1961 and vol. 5, pp. 332-345. 1962.
71. W.E. Hall Jr., “Optimal Control and Filter Synthesis by Eigenvector Decomposition,” Stanford Univ. Dept. of Aero./Astro. Rpt. 436, Ph.D. thesis, 1971.
72. A.J. Laub, “A Schur Method for Solving Algebraic Riccati Equations,” IEEE Trans. Auto. Ctrl., Vol. AC-24, pp. 913-921, 1979.
73. W.E. Holley and A.E. Bryson, “Wind Modelling and Lateral Control for Automatic Landing,” Jour: Spacecraft and Aircraft. vol. 14, no. 2, pp. 65-72, 1977.
74. G. Zames, and B.A. Francis, “Feedback Minimax Sensitivity and Optimal Robustness,” IEEE Trans. Auto. Ctrl., Vol. 28, pp. 585-601, 1983.
75. J.C. Doyle, “Analysis of Feedback Systems with Structured Uncertainty,” Proc. IEEE, vol. 129D. pp. 242-250, 1982.
76. M.G. Safonov, “Robustness and Stability Aspects of Stochastic Multivariable Feedback Design,” MIT Ph.D. thesis, September 1977.
77. J.C. Doyle and G. Stein, “Multi variable Feedback Design: Concepts for a Classical/Modern Synthesis.” IEEE Trans., vol. AC-26, no. 1, 1981.