Abstract
This introductory chapter briefly reviews the evolution of optimal control design. First, it considers the classical control principles of optimal design for ideal completely known systems. Then, the case of incomplete information is studied. The ideas of robust control design and related optimization issues are discussed. The general principles of ellipsoid-based control design are introduced.
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Bibliography
Bellman, R. (1956). Dynamic programming and modern control theory. New York: Academic.
Blanchini, F., & Miami, S. (2008). Set theoretic methods in control. Systems and control: Foundations and applications. Boston, MA: Birkhäuser.
Boltyanski, V., Gamkrelidze, R., & Pontryagin, L. (1956). On the theory of optimal processes. Doklady AN USSR, 110(1), 7–10 (in Russian).
Boltyanski, V., & Poznyak, A. (2012). Robust maximum principle: theory and applications. Boston: Birkhäuser.
Coddington, E., & Levinson, N. (1955). Theory of ordinary differential equations. New York, NY: McGraw-Hill.
Grimble, M. (1994). Robust industrial control. Hemel Hempstead, UK: Prentice Hall International.
Haddad, W., & Chellaboina, V. (2008). Nonlinear Dynamical Systems and Control. Princeton: Princeton University Press.
Ioannou, P., & Sun, J. (1996). Robust adaptive control. Upper Saddle River, NJ: Prentice Hall.
Isidori, A. (1995). Nonlinear control systems. New York, Springer.
Kurzhanski, A., & Valyi, I. (1997). Ellipsoidal calculus for estimation and control. Boston, MA: Birkhäuser.
Maciejowski, J. (1989). Multivariable feedback design. New York: Addison Wesley.
Mahmoud, M. S. (2000). Robust control and filtering for time-delay systems. New York: Marcel Dekker.
Narendra, K. S., & Annaswamy, A. M. (2005). Stable adaptive systems. New York: Dover Publications Inc.
Poznyak, A. (2008). Advanced mathematical tools for automatic control engineers: Deterministic techniques. Amsterdam: Elsevier.
Schweppe, F. (1973). Uncertain dynamic systems. Englewood Cliffs, NJ: Prentice Hall.
Utkin, V. (1992). Sliding modes in control optimization. Berlin: Springer.
Zhou, K., Doyle, J., & Glover, K. (1996). Robust and optimal control. Upper Saddle River, NJ: Prentice Hall.
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Poznyak, A., Polyakov, A., Azhmyakov, V. (2014). Introduction. In: Attractive Ellipsoids in Robust Control. Systems & Control: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-09210-2_1
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DOI: https://doi.org/10.1007/978-3-319-09210-2_1
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Publisher Name: Birkhäuser, Cham
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Online ISBN: 978-3-319-09210-2
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