Conditionally execute a function inside a vector field while integrating with an ODE solver

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Ícar 2021-6-4

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评论： darova 2021-6-7

I am integrating some equations that represent an astrodynamics problem. They are defined by a vector field such as:

where x are the states (e.g. position, velocity, mass...). The dynamics that I'm integrating are fed by a control u, that is computed based on the states and time:

. This control u is computed inside the vector field, which we could explicitely state as

. I am integrating

with an ODE solver (e.g. ode45()), and thus the solver computes the control

at every time step.

Now, what I want is to avoid computing the control

at every time step, but rather only at certain times, with a given frequency (e.g. let's say I want to compute the control at 0.1 Hz, every 10s). How would you recommend me to approach this?

I hope I was clear enough. Thank you for any help.

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Answer 1

darova 2021-6-5

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https://ww2.mathworks.cn/matlabcentral/answers/847720-conditionally-execute-a-function-inside-a-vector-field-while-integrating-with-an-ode-solver#answer_717390

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Try to pass your condition inside ode function

An example

function dy = func1(t,x)
    tset = [10 20 30];
    if any(abs(t-tset)>0.05)
        u = x(1)*t-1;
    end
    % dy function ...
end
function main
    [t,y] = ode45(func1,tspan,x0);
    plot(t,y)
end

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Ícar 2021-6-6

编辑：Ícar 2021-6-6

在 MATLAB Online 中打开

Thanks @darova, seems a feasible option! Will keep the answer opened to see if someone else contributes to the brainstorming.

PS: shouldn't the "any()" expression have a < instead?

if any(abs(t-tset)<0.05)
    ...
end

will execute the control if we are close to a pre-scribed epoch with a resolution of 0.05s.

darova 2021-6-7

will execute the control if we are close to a pre-scribed epoch with a resolution of 0.05s.

You are right, my bad

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Conditionally execute a function inside a vector field while integrating with an ODE solver

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Conditionally execute a function inside a vector field while integrating with an ODE solver

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