MATLAB-如何定义多变量目标优化

我试图理解多变量目标优化，我需要优化复杂函数，但首先，我需要优化以下函数：

function ap_phase = objecfun(tau)

  f = 1000;   %Frequency

  w = 2*pi*f; %Angular Frequency

  trans_func = @(taux) (1-1i*w*taux)./(1+1i*w*taux); %Transfer function   

  trans_zero = trans_func(tau(1)); %Transfer function evaluated with the first variable
  trans_quad = trans_func(tau(2)); %Transfer function evaluated with the second variable

  ap_phase = rad2deg(phase(trans_zero)-phase(trans_quad)); %Phase difference

end

函数objecfun将一个长度为2的向量作为输入，计算2个传递函数，然后减去传递函数的相位

我的目标是相位应该在90度左右

我用来进行优化的脚本如下

tau0 = [2E-5, 1E-3];        %Initial Value for tau(1) and tau(2)
lb = [1E-7, 1E-7];          %Lower bound for tau(1) and tau(2)
ub = [1E-2, 1E-2];          %Upper bound for tau(1) and tau(2)
goal = 90;                  %Optimization goal
weight = 1;                 %Weight
[x,fval] = fgoalattain(@objecfun,tau0,goal,weight,[],[],[],[],lb,ub)

优化器收敛了，但我得到了一个错误的答案

x =

0.0100    0.0000

fval =

-178.1044

那是错误的，fval应该接近90度

---

我做错了什么？

我认为您需要替换您的目标函数和目标值，以便它符合问题公式。您可以使用L2范数作为目标函数，表示函数输出和所需角度之间的差异，并将目标设置为一些公差

我还与fmincon进行了核对：

new_goal = 1e-4;
objectfun = @(x) norm(objecfun(x) - goal);

options = optimoptions('fgoalattain');
options.PlotFcns = 'optimplotfval';
[tau_star,fval] = fgoalattain(objectfun,tau0,new_goal,weight,[],[],[],[],lb,ub,[],options);

options = optimoptions('fmincon');
options.PlotFcns = 'optimplotfval';
[tau_star2,fval,exitflag,output] = fmincon(objectfun,tau0,[],[],[],[],lb,ub,[], options);

fgoalattain_solution_phase_diff = objecfun(tau_star)
fmincon_solution_phase_diff = objecfun(tau_star2)

得到：

fgoalattain_solution_phase_diff =

   90.0000


fmincon_solution_phase_diff =

   90.0006

注：您也可以在函数中省略rad2deg，并使用[rad]中的值作为所需角度