MATLAB: How to return an extra parameter using Matlab’s ODE solvers

odeode45output

I would like to return a parameter, r, from the ode solution, but this parameter is not to be integrated. However, it is important to the result and for later post-processing. I want r to be a vector matching the length of t so I can do 
plot(t, r)
The tricky part for me that seems to stand out from the examples I've looked at here at the forum is that the time dependent variables and their derivatives are dependent on r which in turn r is dependent on a boolean state variable. This means it is rather difficult to calculate r based on the output results from the ode solution variables.
My code is
clear; close all; clf; clc
t_span  = [0 1];
y_0     = [0, 2];
env.g   = 9.81;
figure(101); hold on
options = odeset('AbsTol',1e-6, 'RelTol',1e-6, 'Stats','on');
[t, y] = ode45(@my_ode_fcn, t_span, y_0, options, env);
figure(1)
plot(t, y(:, 1))
xlabel('time, t [s]')
ylabel('position, x [m]')
figure(2)
plot(t, y(:, 2))
xlabel('time, t [s]')
ylabel('velocity, u [m/s]')
function dydt = my_ode_fcn(t, y, env)
    persistent state_flag
    if isempty(state_flag); state_flag=0; end
    x = y(1);
    u = y(2);
    g = env.g;
    if ~state_flag
        r = 20 + 50*t;
    else
        r = 20 + 10*t;
    end
    if (r > 30) && ~state_flag
        state_flag = 1;
        sprintf('State flag = %d', state_flag)
    end
    if (r > 27)
        xdot = 2*u;
        ydot = -g*x;
    else
        xdot = 3*u;
        ydot = -2*g*x;
    end
    figure(101)
    plot(t, r, '*')
    dydt    = zeros(length(y),1);
    dydt(1) = xdot;
    dydt(2) = ydot;
end
I've tried all the suggestions in this thread, but nothing has worked so far:
https://se.mathworks.com/matlabcentral/answers/92701-how-do-i-pass-out-extra-parameters-using-ode23-or-ode45-from-the-matlab-ode-suite
Any syggestions?

Best Answer

If the problems mentioned in my comment are fixed, the solution is easy: Run the integration at first. Then provide the calcualted time and trajectory as input for my_ode_fcn and export the wanted value as 2nd output. Therefore the function must be vectorized - or called in a loop for each time point.
See
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