Are systems considered causal if they depend on prediction of future inputs?

Question

A causal system is a system whose output only depends on the present or the past inputs.

But there are many systems that do a look-ahead prediction and involves that in the calculation.

For example, in autonomous vehicles, the future trajectory of nearby vehicles could be computed and that is used to calculate a control input for the steering system.

I think MPC and and stuff such as receding horizon estimation also depends on estimation of the future state.

In multiple textbooks I've seen the phrase "noncasual systems do not exist in real life". But MPC controllers, look-ahead controllers, etc., are very real.

So are these systems causual or noncausal?

Answer 1

The systems are causal because no matter what a systems does, it gets the current input and has gotten the past inputs so it can only work with past and present inputs and can act based on past and present inputs only. No system can get future inputs.

What it tries to do with those past and present inputs to act now is completely another thing (like video camera frames processed by a computer, doing some math on trajectories, if you are going to hit a pedestrian and should brakes be actuated or not).

Another example is a well-defined system, like a PID controller which has been tuned to the characteristics of the system that are known.

Sort of like when you are boiling water in a kettle, you can sense from the present and past conditions that the water is going to boil soon and you know when to turn down the stove before water boils too vigorously.