optimal quadratic control chapter 2 w&s calculus of extrema
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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. - PowerPoint PPT PresentationTRANSCRIPT
Optimal Quadratic ControlChapter 2 W&S
Calculus of ExtremaDr. Hatem ElaydiEE Department, Islamic University of GazaFeb 18, 2012
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Unconstrained Extrema
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For multivariate functions
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Example 2.1-1
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Back substitution & Lagrange Multiplier
Extrema of functions with equality constraints
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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.
Example 2.2-2
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Lagrange Multiplier Approach
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Example 2.2-2 Using Lagrange
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Solution
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Non-scalar case
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Lagrange Multiplier: Multivariate
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1st variation
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Hessian
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Example 2.2-4
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Solution
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Sol…
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Example 2.2-5
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Solution
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Example 2.2-6
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Nonlinear Programming
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Solution
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Sol…
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2.1, 2.3, 2.7, 2.8
Homework