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Calculus of Variations and Optimal Control

Code: MA563 | L-T-P-C: 3-0-0-6

Prerequisites: MA542 Differential Equations

The concept of variation and its properties, Variational problems with fixed boundaries, The Euler equation, Variational problems in parametric form. Variational problems with moving boundaries, Reflection and refraction extremals. Sufficient conditions for an extremum, Canonical equations and variational principles, Complementary variational principles, The Hamilton-Jacobi equation. Direct methods for variational problems, Rayleigh-Ritz method, Galerkin method. Introduction to optimal control problems, Controllability and optimal control, Isoperimetric problems, Bolza problem, Optimal time of transit, Rocket propulsion problem, Linear autonomous time-optimal control problem, Existence theorems for optimal control problems, Necessary conditions for Optimal controls, The Pontryagin maximum principle.

Texts / References:

  1. A. S. Gupta, Calculus of Variation with Applications, Prentice-Hall, India, 1997.
  2. J. Macki and A. Strauss, Introduction to Optimal Control Theory, UTM, Springer, 1982.
  3. G. M. Ewing, Calculus of Variations with Applications, Dover, 1985.
  4. H. Sagan, Introduction to Calculus of Variations, Dover, 1967.
  5. J. L. Troutman, Variational Calculus and Optimal Control, 2nd edition, Springer Verlag, 1996.