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Optimal Quadratic Control Chapter 2 W&S Calculus of Extrema

Optimal Quadratic Control Chapter 2 W&S Calculus of Extrema. Dr. Hatem Elaydi EE Department, Islamic University of Gaza Feb 18, 2012. Unconstrained Extrema. For multivariate functions. Example 2.1-1. Extrema of functions with equality constraints.

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Optimal Quadratic Control Chapter 2 W&S Calculus of Extrema

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  1. Optimal Quadratic ControlChapter 2 W&SCalculus of Extrema Dr. HatemElaydi EE Department, Islamic University of Gaza Feb 18, 2012

  2. Unconstrained Extrema Dr. H Elaydi, EELE 6302, IUG

  3. Dr. H Elaydi, EELE 6302, IUG

  4. Dr. H Elaydi, EELE 6302, IUG

  5. Dr. H Elaydi, EELE 6302, IUG

  6. For multivariate functions Dr. H Elaydi, EELE 6302, IUG

  7. Example 2.1-1 Dr. H Elaydi, EELE 6302, IUG

  8. Dr. H Elaydi, EELE 6302, IUG

  9. Extrema of functions with equality constraints • Back substitution & Lagrange Multiplier Dr. H Elaydi, EELE 6302, IUG

  10. Dr. H Elaydi, EELE 6302, IUG

  11. Example 2.2-2 • A tin manufacturer wants to maximize the volume of a certain run of cans subject to that the area of tin used be a given constant. If a fixed metal thickness is assumed, a volume of thin constraint implies that the cross-sectional area is constrained. Dr. H Elaydi, EELE 6302, IUG

  12. Dr. H Elaydi, EELE 6302, IUG

  13. Lagrange Multiplier Approach Dr. H Elaydi, EELE 6302, IUG

  14. Dr. H Elaydi, EELE 6302, IUG

  15. Example 2.2-2 Using Lagrange Dr. H Elaydi, EELE 6302, IUG

  16. Solution Dr. H Elaydi, EELE 6302, IUG

  17. Non-scalar case Dr. H Elaydi, EELE 6302, IUG

  18. Lagrange Multiplier: Multivariate Dr. H Elaydi, EELE 6302, IUG

  19. Dr. H Elaydi, EELE 6302, IUG

  20. 1st variation Dr. H Elaydi, EELE 6302, IUG

  21. Dr. H Elaydi, EELE 6302, IUG

  22. Hessian Dr. H Elaydi, EELE 6302, IUG

  23. Example 2.2-4 Dr. H Elaydi, EELE 6302, IUG

  24. Solution Dr. H Elaydi, EELE 6302, IUG

  25. Sol… Dr. H Elaydi, EELE 6302, IUG

  26. Example 2.2-5 Dr. H Elaydi, EELE 6302, IUG

  27. Solution Dr. H Elaydi, EELE 6302, IUG

  28. Example 2.2-6 Dr. H Elaydi, EELE 6302, IUG

  29. Dr. H Elaydi, EELE 6302, IUG

  30. Dr. H Elaydi, EELE 6302, IUG

  31. Nonlinear Programming Dr. H Elaydi, EELE 6302, IUG

  32. Dr. H Elaydi, EELE 6302, IUG

  33. Solution Dr. H Elaydi, EELE 6302, IUG

  34. Sol… Dr. H Elaydi, EELE 6302, IUG

  35. Homework • 2.1, 2.3, 2.7, 2.8 Dr. H Elaydi, EELE 6302, IUG

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