View source for QE2013 AC-3 ECE580-4 - Rhea

[[Category:ECE]]
[[Category:QE]]
[[Category:CNSIP]]
[[Category:problem solving]]
[[Category:automatic control]]
[[Category:optimization]]

=QE2013_AC-3_ECE580-4=

:[[QE2013_AC-3_ECE580-1|Part 1]],[[QE2013_AC-3_ECE580-2|2]],[[QE2013_AC-3_ECE580-3|3]],[[QE2013_AC-3_ECE580-4|4]],[[QE2013_AC-3_ECE580-5|5]]

'''(i)'''
<br> '''Solution: ''' <br>
<math>x(3) = x(2) + 2u(2) = x(1) + 2u(1) + 2u(2) = x(0) + 2u(0) + 2u(1) + 2u(2) </math>

<math>\because x(0) = 3, x(3) = 9 </math>

<math>\therefore \ Constraint: 2u(0) + 2u(1) + 2u(2) = 6 </math>

Let <math>f(u) = u^2(0) + u^2(1) + u^2(2), h(u) = 2u(0) + 2u(1) + 2u(2) - 6 </math>

Let u* be a local minimizer.  Lagrange theorem says there exists a λ such that:

<math>\nabla f(u*) + \lambda \nabla h(u*) = 0 \\
      h(u*) = 0 </math>
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