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Introduction

  • Basil Kouvaritakis
  • Mark Cannon
Chapter
Part of the Advanced Textbooks in Control and Signal Processing book series (C&SP)

Abstract

The benefits of feedback control have been known to mankind for more than 2,000 years and examples of its use can be found in ancient Greece, notably the float regulator of the water clock invented by Ktesibios in about 270 BC,  Vitruvius, The Ten Books on Architecture, 1914, [1]. The formal development of the field as a mathematical tool for the analysis of the behaviour of dynamical systems is much more recent, beginning around 150 years ago when Maxwell published his work on governors Maxwell, Proc. R. Soc. Lond. 16:270–283, 1868, [2]. Since then the field has seen spectacular developments, promoted by the work of mathematicians, engineers and physicists. Laplace, Lyapunov, Kolmogorov, Wiener, Nyquist, Bode, Bellman are just a few of the major contributors to the edifice of what is known today as control theory.

Keywords

Model Predictive Control Markov Chain Model Prediction Horizon Model Predictive Control Algorithm Input Trajectory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Vitruvius, The Ten Books on Architecture (Harvard University Press, Cambridge, 1914)Google Scholar
  2. 2.
    J.C. Maxwell, On governors. Proc. R. Soc. Lond. 16, 270–283 (1868)CrossRefzbMATHGoogle Scholar
  3. 3.
    L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze, E.F. Mishchenko, The Mathematical Theory of Optimal Processes (Interscience, Wiley, 1962)Google Scholar
  4. 4.
    L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze, E.F. Mishchenko, Dynamic Programming (Princeton University Press, Princeton, 1957)Google Scholar
  5. 5.
    H.H. Goldstine, A History of the Calculus of Variations From the 17th Through the 19th Century (Springer, Berlin, 1980)CrossRefzbMATHGoogle Scholar
  6. 6.
    A.E. Bryson, Optimal control—1950 to 1985. IEEE Control Syst. Mag. 16(3), 26–33 (1996)CrossRefGoogle Scholar
  7. 7.
    R.E. Kalman, Contributions to the theory of optimal control. Bol. Soc. Mat. Mexicana 5, 102–119 (1960)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.University of OxfordOxfordUK

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