how to stop ode45 when one of states reach certain value

[x_dot] =derivative(t, x)

x is states [x(1).....x(4)] I need to stop the integration when x(3) reaches 0.1 when the integration stop record (t)

Answer 1

[Jan]

Opt    = odeset('Events', @myEvent);
[T, Y] = ode45(@YourFun, T, Y0, Opt);

function [value, isterminal, direction] = myEvent(T, Y)
value      = (Y(3) == 0.1);
isterminal = 1;   % Stop the integration
direction  = 0;

[J. Alex Lee]

It doesn't seem that your example should work given the limitation that the root-finder for the event relies on crossing zero...in fact I tried a similar example and matlab complained that "sign" is not defined for types logical

This works

function [value, isterminal, direction] = myEvent(T, Y)
value      = (Y(3) == 0.1)-0.5;
isterminal = 1;   % Stop the integration
direction  = 0;

But I have another related question: is it possible to terminate upon meeting ALL conditions, not just ANY:

function [value, isterminal, direction] = myEvent(T, Y)
value      = [(Y(3) == 0.1)-0.5; (x>100)-0.5];
isterminal = ???;   % Stop the integration when the original condition is met AND x > 100
direction  = [0;0];

The goal is to stop integration for a system approaching steady state by checking the magnitude of a derivative in the system; but it may be approached either from the top or the bottom, and that derivative is not monotonic with time so you can detect false positives, so I want to ensure "enough time" has passed before detecting.

[Walter Roberson]

"is it possible to terminate upon meeting ALL conditions, not just ANY"

tolerance = 1e-7;
value = (abs(y(3) - 0.1) < tolerance & abs(x - 100) < tolerance) -0.5;

[J. Alex Lee]

haha, duhhh...thanks

[Alessandro Vitiello]

hi all,

I have this problem, my function is this

function [value, isterminal, direction] = myEvent(t, X)
%err_att = [X(8) X(9) X(10)];
value = ( X(8) == 0.05 )  ;      %X(9) X(10) );
isterminal = 1;               % Stop the integration
direction  = 0;
end

by I have this error :

SWITCH expression must be a scalar or a character vector.

Error in odeevents (line 31)

switch lower(eventFcn)

Error in ode113 (line 148)

odeevents(FcnHandlesUsed,odeFcn,t0,y0,options,varargin);

Error in RLV_assetto (line 62)

[t,X]=ode113('eq_moto_assetto',tt,cond_in,Opt);

please can you help me ??

many many thank for your time and consideration

[Walter Roberson]

Please show the code for building Opt

[James Gilliam]

What is T in this senario and how is it defined? Thanks

[Walter Roberson]

@James Gilliam

In the call

[T, Y] = ode45(@YourFun, T, Y0, Opt);

the input T is the timespan to integrate over. It is a vector that must have at least two elements, but may have more. If it has two elements then ode45() will decide by itself what times to output information at; if it has more than two elements then ode45() will output information at the times given in the vector.

Answer 2

[Walter Roberson]

You need to add an event function. See http://www.mathworks.com/help/matlab/ref/odeset.html#input_argument_d0e709348

[Mohamed Aburakhis]

I found a lot of options , which one should I use?

Answer 3

[Gustavo Lunardon]

This is confusing. In matlab help it says: An event occurs when value(i) is equal to zero. All answers in this post make it value = 1 for the event to happen. Are the answers outdated somehow?

Source: https://nl.mathworks.com/help/matlab/math/ode-event-location.html

[Walter Roberson]

This is a valid concern.

value = (X(8) == 0.05 ) and (Y(3) == 0.1) would happen rarely, when the values were bit-for-bit identical to the representation of 0.05 and 0.1 . One bit different in the representation and the condition will not fire. Better is to write x(8) - 0.05 or 0.05 - x(8), and Y(3)-0.1 or 0.1-Y(3) -- zero crossings can be detected for those.