ode45 and euler not working for random signal

When trying to simulate a first order system subject to a random input that changes value at fixed intervals, neither my ode45 nor euler integration attempts make sense to me. Neither of them follow the inut signal. Please help!

(This code reqs 2016b or later I think)

clc;clear;close all;format compact

w_filt = 10*2*pi; % first order filter

t = linspace(0,1,1000);
dt = t(2)-t(1);
inits = [0];

%% Try ODE 45
Eqns = @(t,s) eqns(t,s,dt,w_filt);
[t,x] = ode45(Eqns,t,inits);

for i = 1:length(t)
    [dx(i,:),ext(i)] = Eqns(t(i),x(i));
end
in = ext;
du = dx;
u = x;

%% Try Euler
X = inits;
for i = 1:length(t)-1
dX(i) = w_filt*(in(i) - X(i));
X(i+1) = du(i)*dt + X(i);
end
dX(end+1) = 0;

%% Plots
figure(1);
title('ODE45');
plot(t,u,t,du,t,in)
legend('u','du','input')


figure(2);
title('Euler Integration')
plot(t,X,t,dX,t,in)
legend('u','du','input')


%% EOM
function [dx,ext] = eqns(t,x,dt,w_relax)
global randval
u =  x;

in = randval;
if rem(t,100*dt) == 0 || t == 0
    in = 0.1*pi/180*(2*rand-1);
    randval = in;
end
du = w_relax*(in - u);

dx = du;
ext = in;
end

[darova]

Can you attach original equations>?

Answer 1

[James Tursa]

You can't use random inputs with ode45( ). ode45( ) relies on the ability to call the derivative function at arbitrary times to control esimated errors. It may even call your derivative function in non-increasing times because of this. It needs the derivatives to be consistent in order for this to work. Having randomness in your derivative function makes the derivatives inconsistent from call to call. ode45( ) will either fail with an error message because it can't get consistent estimated error results, or worse it will give you a garbage answer. You need to use another method besides ode45( ) to solve your stochastic problem.

[SEEmULATER]

Thank you for your response. Your info on ode45 implementation is helpful.

However, you suggest I try another method, which I did: I included a fixed time interval forward euler integration for comparison, which also does not track the input once the steady state is reached.

[James Tursa]

And ...? Are you saying that your Euler scheme is not working, or doesn't give the expected results?

[SEEmULATER]

it does not give the expected results