Optimum Control Problem usingHamiltonian2. min J = SV2 + u? – uq Uz)dt• s. t.y'1 = U1 Y1(0) = 1 y1(2) = 1y'2 = U2 Yz(0) = 2 y½(2)free%3D||%3D%3DEconomic Mathematics

We will first construct the Hamiltonian/Lagrangian then use the Euler-Lagrange equation to solve the…

Answered: Optimum Control Problem using…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Find the order of the given DE. Also, decide if the DE is linear or nonlinear. (a) "+1=ysin(x) (b) y(3) + y = (c) (e*y')'+e-*y = 0 (d) +(- 3x + 2y = 8 %3D
+ Q | CD Page view | A Read aloud | T Add textDraw 9. (a) Perform a qualitative analysis on the following competition model: dy dt dx dt O Search = x(1- x - y) - = y(0.75-y-0.5x) dy dt That is: find the nullclines, the equilibrium values, and draw arrows in each of the regions describing how r and y are changing. (b) Based on your work, in the long-term, if both populations start out at non-zero value, will one population drive the other into extinction or will the populations be able to coexist? 10. (a) Perform a qualitative analysis on the following slightly different competition model: dx dt K = x(1 - x - y) - = y(0.5-0.25y - 0.75x) Highlight (b) Based on your work, in the long-term, if both populations start out at non-zero value, will one population drive the other into extinction or will the populations be able to coexist? 11. (a) Use Euler's method to estimate x(0.3) for the differential equation dr dt 2(1-x) W Erase | 86 881 RE R O A 4) D 3/8/2
2x +y cosxy dx F 2y -x cosxy Exercises 3-4 H.W 1-Evaluate dw at the given value of t: dt 1)- w =x+y X = cost y = sint 2) - 2. W =x" + y X = cost + sint y = cost -sint 3)- y W =-+ = cos't y = sin't x = Z =- w = In (x² +y² +z²) z = 4VE 4)- X = cost y = sint 5) - w = 2ye* -In z x = In (1 +1) y = tant z =e' 6)- w =z - sinxy y = Int x =t
+メ Exorcise 1: For the H PF. state ewation whelner the is ordinary or partial, Nonlinear Linear or d its order. 1. y = メリ+1 Jく 2. yy" +y't y's I 3. %3D 4. edy dメ2 5 day + メy+り=2 トd Siny dx4 a6) dy ta(x)y %3D to + dy
0 V3 0 | for Imagine a Hamiltonian is represented by a matrix, of the form H = 2 V3 0 3 e state y : 2i |. Find the average value of H for this given state, y.
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plz solve only 3rd within 30-40 mins I'll give you multiple upvote
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1)ODE SOLVER
Q2. Consider the function xy+ x'y- xy a. Find the critical points of f(x,y) b. Write the Hessian matrix c. Classify the critical points obtained in part (a) as local maxima, local minima, saddle point or can't tell by evaluating the Hessian matrix at these points

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Optimum Control Problem using Hamiltonian 2. min J= (y2 + uj – U1Uz)dt • s. t. y's У1 3 и, У1 (0) — 1 у, (2) — 1 %3D y'2 = u2 Yz(0) = 2 y2(2) free %3D Economic Mathematics