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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> A Moving to another question will save this response. Question 3 AM The general solution of y"-xy'+ (x- 24 y = 0, is: Oa C,xJ,(x) + C,xJ_,x) Ob. OcC,,(3x) + C,xJ_(3x) Od C;xJ,) + C,xY,(x) Oe C,xJ,(4x) + C,x Y,(4x) A Moving to another question will save this response. Type here to search
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
y′ = e−t + y
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
Known system state equation and initial state i, = u, i, = x, Find the minimum of with respected to u'(1).
Hi could you please help me with this practise problem, with huge emphasis on explanation of finding the bounds for the integrals please.
Given an IVP d"y + an-1(x) dn-ly dy +...+ a1 (x) dx + ao (x)y = g(x) drr-1 у (хо) — Уо, у (tо) — Ул, -.., у" "(2о) — Ул-1 If the coefficients an (x), ..., ao (x) and the right hand side of the equation g(x) are continuous on an interval I and if an (x) +0 on I then the IVP has a unique solution for the point xo e I that exists on the whole interval I. Consider the IVP on the whole real line d'y - 36) dx4 dy + y= sin(x) 1 (x² dz3 x2 + 36 dx у(3) — 916, у (3) — 14, у"(3) — 8, у" (3) — 8, The Fundamental Existence Theorem for Linear Differential Equations guarantees the existence of a unique solution on the interval
2. Using the linear model of a researcher calculated the hat-matrix = X(X'X)¯¹X' = H = TA [0.2516 0.1101 0.3931 0.1101 0.2044 0.0157 0.3931 0.1572 0.7704 0.0535 0.2421 -0.1352 0.1101 0.2044 0.0157 0.2421 0.0818 0.2232 -0.0597 0.2799 (a) Estimate o. That is, find Residual Standard Error s. /1.) zachy UNDI Yevevi TA' y = Bo + Br2 + H and the residual e using 6 observations. vull lalg 0.0818 0.0534 0.1101 0.2421 0.2044 0.2233 -0.1352 0.0157 -0.0597 0.3176 0.2421 0.2233 0.2044 0.22327 0.2233 0.2516 SOUD DAN wuc. " e = -0.02 0.12 -0.56 0.88 -0.01 [-0.07]

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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