keeping a shared parameter across data sets when estimating parameters

Question

SP 2018-4-21

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/396398-keeping-a-shared-parameter-across-data-sets-when-estimating-parameters

I am trying to fit data to a non linear ODE system in order to estimate model parameters. I have data for three separate subjects as data1,data2,data3 measured over the same time span. In estimating these parameters I want to keep one of the estimated parameters to be common among all subjects.

I have written the code similar to the one at 'anlaysis.m' in here .

But, still I am getting a different value for the parameter that I want to keep constant.

My code is something like:

%Y has 4 columns. First column is time. Second column is data on 
%first subject (data1), third colum is data on second subject (data2)
%third column is data on third subject (data3)
[fit,fval]=fmincon(@(parameters)ssq(parameters,Y),initial,[],[],[],[],lb,ub,[])
function SSE=ssq(parameters,Y)
    time=Y(:,1);
    SSE=0;
      for i=1:3
          fitted=model(parameters,time,i);
          error1=fitted(:,1)-Y(:,i+1);
          SSE1=sum(error1.^2);
          SSE=SSE+SSE1;
      end     
  end
function output= model(parameters,t,subject)
    t=t(1:9)';   
    x0=[10^5,0.01];
      a_1=parameters(1);%dependent on subject
      a_2=parameters(2);%dependent on subject
      a_3=parameters(3);%dependent on subject
      r1=parameters(4);%common to all subjects
      if subject==1
          parameters1=[a_1,r1];
          [time,pred1] = ode45(@(t,y)Equations(t,y,parameters1),t,x0,options);
          output=pred1;
      end
      if subject==2
         parameters2=[a_2,r1];
         [time,pred2] = ode45(@(t,y)Equations(t,y,parameters2),t,x0,options);
         output=pred2;
      end
      if subject==3
           parameters3=[a_3,r1];
           [time,pred3] = ode45(@(t,y)Equations(t,y,parameters3),t,x0,options);
           output=pred3;
      end
      function s=Equations(t,y,eval)
      s=zeros(2,1);
      % b, k are know  constant parameter values. The parameter estimated as
      % eval(2) should be constant among all subjects
      s(1)=(eval(2)*y(1))-eval(1)*y(2)*y(1);
      s(2)=b*(k-y(2))*y(1)-eval(1)*y(2);
      end
end

Can someone please explain to me how I can correct the code to evaluate a common parameter as I don't know if it works because it has been running for a very long time? Here, although at the moment I have written it to 3 subjects I actually ahve 10 subjects. So, I need to find an efficient way to deal with this.