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The inverted pendulum problem is a famous control task. It can be solved with a technique called system identification. System identification means to formalize the state-action space of a system in a model and this model is used to predict future states. It is similar to creating a physics engine. This is done with data from the past. For example, the behavior of a domain is analyzed from timeframe 0 to 1000. And the generated model is used to control the system from timeframe 1000 to 10000.

The underlying assumption is, that the model remains the constant. That means, that the system can be identified once and it will work the same in the future. Or to explain it more colloquial, that the past will repeat over and over again. For a mechanical system this is equal to the law of physics, which are remaining constant over time. That means, it's not important in which timeframe an action is executed in the system, because the system will react always the same.

My question is: Has this assumption an official term? Are systems available which are not repeating themself?

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  • $\begingroup$ The term you're looking for is 'time-varying', as opposed to 'time-invariant'. $\endgroup$ – Steve Heim Aug 5 at 15:22

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