Using fminsearch and then using the output of fminsearch in cost and ode function.

Using initial value of -100 for fminsearch, After obtaining optimal value of lambda by fminsearch, how to use the output of fminsearch in function?How to remove the error?

%main file 
close all;  
clc;  
clear;
  
[lambdas,cost] = fminsearch( @(x) Q1_cost, [ -100 ] ); 

Not enough input arguments.

Error in solution>Q1_cost (line 14)
[interval,sol] = ode45( @(t,x)Q1_ode,[0,10], [0.5;lambdas] );

Error in solution (line 6)
[lambdas,cost] = fminsearch( @(x) Q1_cost, [ -100 ] );

Error in fminsearch (line 201)
fv(:,1) = funfcn(x,varargin{:});

J_min=HW1_Q4_a_J_min_fn(lambdas); 
[interval, sol] = ode45( @(t,x) Q1_ode(t,x), [t_0,t_f], [0.5;lambdas] ); 


 % file named with Q1_cost
function [J] = Q1_cost(lambdas)  

[interval,sol] = ode45( @(t,x)Q1_ode,[0,10], [0.5;lambdas] ); 
  
lambda_t = sol(:,2);  

J = lambda_t(end)^2;  
 
end


% file named with Q1_ode
function [xdot] = Q1_ode(t,x) 
  
n = length(x);  
xdot = zeros(n,1); % x = [ v(t), gamma(t), h(t) ]  
  
x_1     = x(1);  
lambda_0= x(2);   
  
u=log((-1+(x_1/0.8))/(0.015*lambda_0*exp(0.01*t)))

xdot(1) = -0.02*x_1+0.015*u 
xdot(2) = (1-exp(u))*2*(x_1/0.8)*(1/0.8)*exp(-0.01*t)-0.015*lambda_0; 
  
end 

Answer 1

[Sam Chak]

Maybe like this:

[lambdas, cost] = fminsearch(@Q1_cost, -100)

lambdas = -0.0411

cost = 264.3093

[interval, sol] = ode45(@Q1_ode, [0 10], [0.5 lambdas]);
plot(interval, sol(:,2))

% Cost 
function [J] = Q1_cost(lambdas)
    [interval,sol] = ode45(@Q1_ode, [0 10], [0.5 lambdas]); 
    lambda_t = sol(:,2);  
    J = lambda_t(end)^2;
end

% ODEs
function xdot = Q1_ode(t,x) 
    xdot = zeros(2, 1); % x = [ v(t), gamma(t), h(t) ]  
    x_1      = x(1);  
    lambda_0 = x(2);   
    u        = log((-1+(x_1/0.8))/(0.015*lambda_0*exp(0.01*t)));
    xdot(1)  = -0.02*x_1+0.015*u;
    xdot(2)  = (1-exp(u))*2*(x_1/0.8)*(1/0.8)*exp(-0.01*t)-0.015*lambda_0;   
end