ODE Events Function Using Persistent Variables

Hi all,

I am solving an ODE with an events function, which requires that it gets stopped after a certain criterion is reached in its response, which can only be determined by employing the previous values of the ODE's solution. To demonstrate that problem I have written this simple code below.

The only way I could think of achieving my above objective was by using persistent variables in the ODE events function. This allows me to keep the previous values of the solution whilst the ODE is being solved, and thus terminate it when the specific criterion is reached.

However I run into the following problem: Every time I run the script, either to debug or for any other purpose, the persistent variables are not cleared. So I have to clear them manually, and the process becomes quite tedious, and prone to error as I forget to clear all the appropriate ones some times. I have looked in to how I can clear those variables in the eventsfcn function, however I do not think that its possible to do that automatically.

Hence my question comes in two parts:

1. Can I clear the persistent variables automatically before I run my code every time?
2. In case not, is there a better way to achieve my above objective by not utilising persistent variables?

clear ; clc

m = 10 ;
k = 10 ;
f = 10 ;
tol = 1e-3 ;

opts = odeset('Events', @(t, y) eventfcn(t, y, tol)) ;
tspan = [0 10];
y0 = [1 0];

sol = ode15s(@(t, y) odefcn(t, y, m, k, f), tspan, y0, opts);

% Figure
figure
    plot(sol.x, sol.y(2,:))

% Events Function
function [v, i, d] = eventfcn(t, y, tol)

    persistent Y n
    if isempty(n)
        n = 0 ;
        Y = 0 ;
    end
    n = n + 1 ;
    Y(n) = y(2) ;

    if numel(Y) > 2
        err = diff(Y(end-1:end))/Y(end) ; % ERROR CRITERION TO STOP SOLVER
    else
       err = nan ;
    end   
    
if err <= tol
    v = 0 ;
else
    v = 1 ;
end

i = 1 ; % Halt integration
d = 0 ; % Zero can be approached from any direction
end

% ODE Function
function dydt = odefcn(t, y, m, k, f)

dydt = [y(1) ; -(k*y(2) - f)/m] ;

end

Answer 1

[Steven Lord]

IMO persistent variables is not the right technique to use. One reason why is that the solver does not always evaluate your function with a time that is later than the previous evaluation. If it finds that the error estimate is not within tolerances, it may reject that time step and evaluate your function at an earlier time. So your event function may be comparing the current results against potential future results, not previous results!

What you have is more of a delay differential equation, and for that I'd use the dde23 solver or the ddesd solver. While your ddefun input would not use the "history" input Z the events function you specify in the options structure would.

[KostasK]

I undesrtand your point on the shortcommings of using a persistent variable.

On the other side, the DDE does not seem to have the same variety of solvers as the ODE suit, and in spceific the ODE23t which is the one that works for my case.

[Ameer Hamza]

Although it is correct that odexx() functions can move forward and backward in time when evaluating the ODE function, but the same thing does not apply to the event function. Inside the event function, the time is always increasing, so the current method use by OP will work.

[KostasK]

^^ that is really important info, have you performed any tests on that?

[Ameer Hamza]

Yes. I tried it. ODE event function is only called once a step-size is decided in the current iteration, so it will only move in the forward direction.

Answer 2

[Ameer Hamza]

Run

clear functions

to re-initialize all the persistent variables.

[KostasK]

Does it work for you? Doesn't seem to work for me when I use it after the first line of my code such that

clear ; clc
clear functions

[Ameer Hamza]

There does seem to be some issue. Putting

clear functions

inside script does not seems to work everytime. But running it in command window works. This might be a bug.