Calculus of variations and control

Chapter I: Calculus of variations

1. Overview. Keynote examples. Problem statement. Concept of solution. Problems with no solution

2. Minimal background on functional analysis. Weierstrass-Hilbert-Tonelli minimization theorem

3. Minimal background on measure theory. Existence of solutions

4. Basic approximation schemes: Ritz method and finite differences

5. Necessary optimality condition: Euler-Lagrange equations

6. The general variation of a functional. Endpoints on curves

7. Broken extremals: Weierstrass-Erdmann conditions

8. The variational derivative and the isoperimetric problem

9. Numerical solution workshop

10. Complements: global constraints, nonsmooth solutions and second-order conditions

 

Chapter II: Control (by Prof. Eduardo Cerpa)

 

Bibliography:

Gelfand, IM; Fomin, SV. “Calculus of Variations.” Prentice-Hall, Inc., Englewood Cliffs, NJ 1963.

Álvarez, F. “Cálculo de Variaciones.” II Escuela de Verano MECESUP 2002, DIM-UCH.

Peypouquet, J. “Optimización y Sistemas dinámicos.” Ediciones IVIC, 2013.