SwitchedSystem: event_variable_equation

[narr95]

I'm trying to model a switched system where the state dynamic is described by an equation like this:

where: x is the state vector that consists of the elements x1 and x2 and Ai is a matrix 2x2. i = 1, 2, 3 then I have a system with 3 different modes. Assuming that at t=0 the state follows the first mode (i=1) and that, after a given time, if x1 >= 10, the system enters in the second mode (i=1), whereas if x2 >= 5 the system enters the third mode. My question is: is it possible to write the "event_variable_equation" parameter to model this system? If not, is it possible to use the more general class DiscontinuousSystem to model this system?

[sixpearls]

Hi @narr95, based on what you're describing you could use a standard DynamicalSystem object to implement the model you're after. You may want a state equation of the form:

def state_equation(t, x):
    x1, x2 = x
    if x1 >= 10:
        return A2 @ x
    elif x2 >= 5:
        return A3 @ x
    else:
        return A1 @ x

Note that you may want to verify the logic of your model, but hopefully this can get you started. I'm assuming the "A" matrices are intended to be the "state matrix" for each mode, i.e., xdot = Ai x for each mode i.