Optimize cost function to obtain optimal value of the optimization variable.

Question

Yokuna 2022-10-3

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1816270-optimize-cost-function-to-obtain-optimal-value-of-the-optimization-variable

评论： Torsten 2022-10-3

采纳的回答： Walter Roberson

The problem is to find a and b such that the cost function

is minimized. The cost function

is defined as,

The dynamical equations are:

I tried to use the ode45 to solve the the dynamical equations but was unable to solve using the ode45 as it has a and b also as variables, which are needed to optimize the cost function. Can someone help to solve the equations by ode45 and minimize the cost function at the same time? I am trying to use fminsearch but how to use it?

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Answer 1

Walter Roberson 2022-10-3

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https://ww2.mathworks.cn/matlabcentral/answers/1816270-optimize-cost-function-to-obtain-optimal-value-of-the-optimization-variable#answer_1065425

Create a function that accepts a and b and uses ode45() to run the system to tspan 10. Return the values of y1(end) and y2(end) for those particular a and b

Now write a caller to that function that accepts a vector of two values, a and b, runs the function mentioned above, calculates C and returns the value.

Now use fminunc() or fmincon() on that second function. The vector of coordinates that minimizes the function will be the a and b values you are looking for.

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Walter Roberson 2022-10-3

在 MATLAB Online 中打开

init_ab = [0 1];
best_ab = fminunc(@cost_ab, init_ab);
a = best_ab(1); b = best_ab(2);
function cost = cost_ab(ab)
   [t,y]=ode45(@(t,y) ques1(t,y,ab(1),ab(2)), [0 10], [1,2]');
   cost = (y(end,1) - 1500).^2 + (y(end,2) - pi/2).^2;
end

Torsten 2022-10-3

在 MATLAB Online 中打开

init_ab = [0 1];
[best_ab,cost] = fminunc(@cost_ab, init_ab)
Local minimum possible.

fminunc stopped because it cannot decrease the objective function
along the current search direction.
best_ab = 1×2
    0.8611   -0.1213
cost = 2.1954e+06
a = best_ab(1); b = best_ab(2);
function cost = cost_ab(ab)
   ques1 = @(t,y)[cos(ab(1)+ab(2)*t)-sin(y(2));(sin(ab(1)+ab(2)*t)-cos(y(2)))/y(1)];
   [t,y]=ode45(ques1, [0 10], [1,2]');
   cost = (y(end,1) - 1500).^2 + (y(end,2) - pi/2).^2;
end