Dynamic systems with delays


In which measure would it be possible to use a dynamic model with delays such as x_dot(t) = A x(t) + B u (t - tau)? Will it be possible in the future?

Thank you!


You could propagate your current state by tau outside of your solver with your model, and use the predicted state to initialize the solver. That way the input is ready for the correct state, since tau seconds will have passed and your ‘future’ state will be your current state at the instant you apply your input. You will have to hold your input over the prediction, since you don’t know it yet. But from experience it works well for small taus.

There are probably other more sophisticated methods, but you could try this to start.


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Thank you Christian for your reply!
I’ll check if this can work out.