Basic Concepts of Discrete-Time Optimal Control Theory

  • M. Drouin
  • H. Abou-Kandil
  • M. Mariton
Part of the Applied Information Technology book series (AITE)


Before going into the details of the new hierarchical method that constitutes the central topic of the present monograph, some information on the more general framework of the book should be provided. This is the purpose of this chapter.


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  1. Anderson B.D.O., J.B. Moore, Linear optimal control, Prentice-Hall, London, 1971.zbMATHGoogle Scholar
  2. Arrow K.J., L. Hurwicz, H. Uzawa, Studies in linear and non-linear programming, Stanford University Press, Stanford, 1968.Google Scholar
  3. Ashworth M.J., Feedback design of systems with significant uncertainties, John Wiley, London, 1982.Google Scholar
  4. Athans M., P.L. Falb, Optimal control: An introduction to the theory and its applications, McGraw Hill, New York, 1966.Google Scholar
  5. Bellman R., Dynamic programming, Princeton University Press, New Jersey, 1957.Google Scholar
  6. Bellman R., S.E. Dreyfus, Applied dynamic programming, Princeton University Press, New Jersey, 1962.Google Scholar
  7. Bellman R., R. Kalaba, Quasi-linearization and non-linear boundary-value problems, Rand Corporation, 1965.Google Scholar
  8. Boudarel R., J. Delmas, P. Guichet, Commande optimale des processus, Vol. 2, Programmation non-linéaire et ses applications, Dunod, Paris, 1968.zbMATHGoogle Scholar
  9. Brockett R.W., Finite dimensional linear systems, John Wiley, New York, 1970.zbMATHGoogle Scholar
  10. Caratheodory C., Calculus of variations and partial differential equations, Vol. 1 and 2, Holden Day, Trans. 1967.Google Scholar
  11. Dreyfus S.E., Dynamic programming and the calculus of variations, Academic Press, New York, 1965.zbMATHGoogle Scholar
  12. Euler L., Insitutionum calculi integralis volumen tertium, cum appendice de calculo variationum, Acad. Imp. Scient., Petropoli, pp. 459–596, 1770.Google Scholar
  13. Eykhoff P., P. Grinten, H. Kwakernaak, B. Veltman, Systems modelling and identification, IFAC World Congress, 1966.Google Scholar
  14. Falb P.L., J.L. De Jong, Some successive approximation methods in control and oscillation theory, Academic Press, New York, 1969.zbMATHGoogle Scholar
  15. Fliess M., Un outil algébrique: les séries formelles non commutatives, in Mathematical System Theory, G. Marchesini and S.K. Mitter eds., Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, New York, 1976.Google Scholar
  16. Fliess M., Lie Brackets and optimal non-linear feedback regulation, IFAC World Congress, Budapest, 1984.Google Scholar
  17. Hadley D., Non-Linear and dynamic programming, Addison Wesley, New York, 1964.Google Scholar
  18. Halkin H., A maximum principle of the Pontryagin type for systems described by non-linear difference equation, SIAM J. Control, no 4, pp. 90–111, 1966.MathSciNetzbMATHGoogle Scholar
  19. Halme A., and co-authors, On synthesizing a state regulator for analytic non-linear discrete-time systems, Int. J. Control, Vol. 20, pp. 497–515, 1974.MathSciNetzbMATHCrossRefGoogle Scholar
  20. Halme A., R.P. Hamalainen, On the non-linear regulator problem, JOTA, Vol. 16, pp. 255–275, 1975.Google Scholar
  21. Jamshidi M., An overview on the solutions of the algebraic matrix Riccati equation and related problems, Large Scale Systems 1, pp. 167–1972, 1980.MathSciNetzbMATHGoogle Scholar
  22. Kalman R.E., Contribution to the theory of optimal control, Bol. Soc. Mat. Mexicana, pp. 102–119. 1960.Google Scholar
  23. Kalman R.E., P.L. Falb, M.A. Arbib, Topics in mathematical system theory, MacGraw-Hill, New York, 1969.zbMATHGoogle Scholar
  24. Kucera V., A review of the matrix Riccati equation, Kybernetica, Vol. 9, n° 1, pp. 44–61, 1973.Google Scholar
  25. Kuhn W., A.W. Tucker, Non-linear programming, Proc. 2nd Berkeley Symp. on Math. Stat. Prob., 1955.Google Scholar
  26. Kwakernaak H., R. Sivan, Linear optimal control systems, John Wiley, New York, 1971.Google Scholar
  27. Lagrange J.L., Leçons sur le calcul des fonctions, Coucier, Paris, 1806.Google Scholar
  28. Lang B. and co-authors, Decentralized calculations in optimal control of a large thermic process: methods and results, IFAC Symp. LSSTA, Toulouse, France, pp. 505–506, 1980.Google Scholar
  29. Lee B.E., L. Markus, Foundations of optimal control Theory, John Wiley, New York, 1967.zbMATHGoogle Scholar
  30. Leitman G., An introduction to optimal control, McGraw-Hill, New York, 1966.Google Scholar
  31. Lhote F., J.C. Miellou, Algorithmes de décentralisation et de coordination par relaxation en commande optimale, in Analyse et commande des systèmes complexes, A. Titli Ed., Cepadues, Toulouse, 1979.Google Scholar
  32. Luenberger D.G., Optimization by vector space methods, John Wiley, New York, 1969.zbMATHGoogle Scholar
  33. Pontryagin L.S., V.G. Boltyanski, R. V. Gamkreljdze, E.F. Mischenko, The mathematical theory of optimal processes, Interscience, New York, 1962.Google Scholar
  34. Sage A.P., Optimum system control, Prentice-Hall, New York, 1969.Google Scholar
  35. Singh M.G., Dynamical hierarchical control, North Holland, Amsterdam, 1977.Google Scholar
  36. Singh M.G., A. Titli, Systems: decomposition, optimization and control, Pergamon Press, Oxford, 1978.Google Scholar
  37. Special Issue on Linear-Quadratic-Gaussian Problem, M. Athans Ed., IEEE Trans. AC-16, n° 6, 1971.Google Scholar
  38. Titli A., Contribution à l’étude des structures de commande hiérarchisée en vue de l’optimisation des processus complexes, Thèse Docteur d’Etat, Université Paul Sabatier, Toulouse, 1972.Google Scholar
  39. Varayia P.P., Notes on optimization, Van Nostrand Reinhold Co., New York, 1972.Google Scholar
  40. Wonham W.M., C.D. Johnson, Optimal bang-bang control with quadratic performance index, Trans. ASME, Vol. 86, pp. 107–115, 1964.CrossRefGoogle Scholar
  41. Zadeh L., C.A. Desoer, Linear system theory, McGraw-Hill, New York,1963.Google Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • M. Drouin
    • 1
  • H. Abou-Kandil
    • 1
  • M. Mariton
    • 2
  1. 1.University of Paris VI and Laboratory of Signals and SystemsGif-sur-YvetteFrance
  2. 2.MATRA SEP Imagerie et Informatique and Laboratory of Signals and SystemsGif-sur-YvetteFrance

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