Practice Final Exam

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April 03, 2023, at 01:34 PM by 10.35.117.248 -
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Final Exam 2015

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April 03, 2023, at 04:51 AM by 136.36.4.38 -
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(:toggle hide gekko button show="Show GEKKO (Python) Code":) (:div id=gekko:) (:source lang=python:) import numpy as np from gekko import GEKKO

  1. Check solution with GEKKO

m = GEKKO() m.time=[0,1] u = m.Var(value=1) x = m.Var(value=0) m.Obj((x-3)**2) m.Equation(5*x.dt()==-x+2*u) m.options.IMODE = 6 m.options.NODES = 3 m.solve()

  1. Matrix solution for Orthogonal Collocation on Finite Elements
  3. min (x-3)^2
  4. s.t. 5 * dx/dt = -x + 2 * u
  6. Equations 1-2 (subject to equations at each node)
  7. 5 * xdot1 = -x1 + 2*u1
  8. 5 * xdot2 = -x2 + 2*u2
  9. Equations 3-4 (collocation equations)
  10. t2 * 0.75 * xdot1 - t2 * 0.25 * xdot2 = x1 - x0
  11. t2 * 1.00 * xdot1 = x2 - x0
  12. Equations 5-6 (derivative of objective = 0)
  13. 2 * (x1-3) = 0
  14. 2 * (x2-3) = 0
  16. Rearrange to put all variables on left-hand side
  17. Equations 1-2 (subject to equations at each node)
  18. 5 * xdot1 + x1 - 2*u1 = 0
  19. 5 * xdot2 + x2 - 2*u2 = 0
  20. Equations 3-4 (collocation equations)
  21. t2 * 0.75 * xdot1 - t2 * 0.25 * xdot2 - x1 = -x0
  22. t2 * 1.00 * xdot1 - x2 = -x0
  23. Equations 5-6 (derivative of objective = 0)
  24. 2 * x1 = 6
  25. 2 * x2 = 6
  27. Set-up and solve A y = b
  28. y = [xdot1 xdot2 x1 x2 u1 u2]
  29. Matrix A

A = np.array()

  1. Column vector b

b = np.array([0,0,0,0,6,6])

  1. Solve A y = b as y = A^-1 * b

ymat = np.linalg.solve(A,b)

print('Variables with Orthogonal Collocation') print(['u1 = ' + str(ymat[4])]) print(['u2 = ' + str(ymat[5]) + ' (Matrix) vs ' + str(u.value[-1]) + ' (GEKKO)']) print(['x1 = ' + str(ymat[2])]) print(['x2 = ' + str(ymat[3]) + ' (Matrix) vs ' + str(x.value[-1]) + ' (GEKKO)']) print(' ') print('Derivatives with Orthogonal Collocation') print(['d(x11)/dt = ' + str(ymat[0])]) print(['d(x21)/dt = ' + str(ymat[1])]) (:sourceend:) (:divend:)

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March 23, 2018, at 03:42 PM by 10.5.113.167 -
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Solution 3

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March 23, 2018, at 01:46 PM by 10.5.113.167 -
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(:title 2015 Final Exam for Dynamic Optimization:)

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(:title Practice Final Exam:)

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Attach:inverted_pendulum2.gif Δ

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March 22, 2018, at 08:44 PM by 10.5.113.167 -
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Attach:inverted_pendulum2.gif Δ

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Solution

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Solution 1

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See Inverted Pendulum Solution

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Solution 2

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Solution 3

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See Inverted Pendulum Solution

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March 21, 2016, at 03:45 PM by 45.56.3.173 -
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February 09, 2016, at 09:55 PM by 174.148.97.76 -
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(:title Final Exam for Dynamic Optimization:)

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(:title 2015 Final Exam for Dynamic Optimization:)

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(:description Final exam for the graduate level course on dynamic estimation and optimization.:)

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(:description Final exam for the graduate level course on dynamic estimation and optimization in 2015.:)

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February 09, 2016, at 09:53 PM by 174.148.97.76 -
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Final Exam

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Final Exam 2015

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June 15, 2015, at 02:27 PM by 45.56.3.184 -
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Solution

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June 05, 2015, at 11:15 PM by 10.5.113.170 -
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(:title Midterm Exam for Dynamic Optimization:) (:keywords Python, MATLAB, Simulink, nonlinear control, model predictive control, exam, midterm:) (:description Mid-term exam for dynamic estimation and optimization as a graduate-level course.:)

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(:title Final Exam for Dynamic Optimization:) (:keywords Python, MATLAB, Simulink, nonlinear control, model predictive control, exam, final:) (:description Final exam for the graduate level course on dynamic estimation and optimization.:)

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(:title Midterm Exam for Dynamic Optimization:) (:keywords Python, MATLAB, Simulink, nonlinear control, model predictive control, exam, midterm:) (:description Mid-term exam for dynamic estimation and optimization as a graduate-level course.:)

Final Exam

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