ESZA006-13 Optimal Control Theory (3-0-4)
Syllabus:
Introduction to the Calculus of Variations. Fundamental Lemma of the Calculus of Variations. The
Euler-Lagrange equation in the basic problem of the Calculus of Variations. Functionals depending
on higher-order derivatives; variational problem for many-variable functionals; Euler-Poisson
equation. Applications of the Calculus of Variations. Problem-solving examples. Variational
problems with conditional extrema. Optimization of dynamical systems, Pontryagin’s maximum
principle. Least-time problem. Dynamic programming, Bellman’s principle, the Hamilton-JacobiBellman equation. Optimal systems based on quadratic performance indices: the linear-quadratic
regulator.
Prerequisites:
Instrumentation and Control.
Required texts:
● LEITMANN, G. The Calculus of Variations and Optimal Control: An Introduction. New York: Plenum
Press, 1981.
● NAIDU D.S. Optimal control systems. Boca Raton, FL: CRC Press, 2002.
Additional texts:
● LEWIS, F.L.; SYRMOS, V.L. Optimal control. 2nd ed. New York: Wiley, 1995.
● KIRK, D.E. Optimal Control Theory: An Introduction. Englewood Cliffs: Prentice-Hall, 1970.
Republished by Dover, 2004.
● BRYSON, A.E., Jr.; Ho, Y.-C. Applied Optimal Control, Optimization, Estimation and Control.
Boca Raton, FL: Taylor & Francis, 1987.
Further Bibliography:
● ELSGOLTS, L. Differential Equations and the Calculus of Variations. Moscow: Mir, 1977.
● KRASNOV, M.L.; MAKARENKO, G.I.; KISELIOV, A.I. Cálculo Variacional (Calculus of Variations ¾ in
Portuguese). Moscow: Mir, 1984.
● BAUMEISTER, J.; LEITÃO, A. Introdução à Teoria do Controle e Programação Dinâmica
(Introduction to Control Theory & Dynamical Programming ¾ in Portuguese only). Rio de Janeiro:
IMPA, 2008.