Calculus Variational; code for finding the value of two constants for 2 values of the variable

Question

Viorica Alina 2024-1-20

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2072366-calculus-variational-code-for-finding-the-value-of-two-constants-for-2-values-of-the-variable

评论： Dyuman Joshi 2024-1-22

Hello,

I want to write a code for Calculus Variational problem. I have to find the extremals this equation J = $(0->1) [diff(x,t)^2+10*t*x]dt

After the Euler equation, I found x(t) == (5*t^3)/6 + c1*t + c2; but here I didn't suceed in writing the code for calculating c1 and c2 for t=0 and t=1.

Is there a chance for anyone to help me?

Thank you,

% optimal control course
%Example: optimal control problem, min J = $(0->1) [diff(x,t)^2+10*t*x]dt
%boundary conditions: x(0) = 1, x(1)=2;
%dsolve – solve differential equations
%solve – solve algebraic equations
%solve differential equations (Euler – Lagrange equations)
syms x(t)
f = diff(x,t)^2+10*t*x;
G = functionalDerivative(f,x)
%solve differential equations (Euler – Lagrange equations)
syms x(t)
eqns =[ x(t) == (5*t^3)/6 + c1*t + c2];
%solve algebraic equations by applying boundary conditions
syms t0 tf
t0=0
tf=1
SS = solve(eqns);
c1 = SS.c1;
c2 = SS.c2;

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Answer 1

Paul 2024-1-20

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2072366-calculus-variational-code-for-finding-the-value-of-two-constants-for-2-values-of-the-variable#answer_1393461

在 MATLAB Online 中打开

Boundary conditions can be specified in the call to dsolve

syms x(t)

f = diff(x,t)^2+10*t*x

f(t) =

eqn = functionalDerivative(f,x) == 0

eqn(t) =

sol = dsolve(eqn,x(0)==1,x(1)==2)

sol =

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Viorica Alina 2024-1-21

Thank you very much; this is perfect!!!

Dyuman Joshi 2024-1-22

Hello @Viorica Alina, if this answer solved your problem, please consider accepting the answer.

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