Hi! I´m receiving the control error from a plant in an adpative system. In the context of my research, the control error is observed as a random sequence which its value depends on the parameters estimated the time before (so the parametric error is also a random sequence). The goal is to make the error behave as a desired distribution, so I need to create a decision mechanism which works with random variables and returns a deterministic answer to be used on the plant.
To achieve this, I considered necessary to compare the objective distribution with one generated with the fist N samples of control error (which by now has one dimension). In this context: do you that using Wasserstein metric can get info about the mean, and usin KL divergence I can have an idea of which distribution is better?Could it be considered as the performance index of my adaptive system?
I really appreciate and thank some guidance and suggestions about this idea. Have a good day!
It is not entirely clear what do you want to achieve.
If you want to determine if you sample corresponds to the "objective" distribution you can use one of the tests that measure goodness-of fit
- Kolmogorov-Smirnov
- Anderson-Darling
- chi squared
If you want to check if a certain statistic (often the mean for sample) corresponds to the parameter of "objective" distribution you can use some of test statistics that measure
distance of a statistic from the parameter of the "objective" distribution (often \mu if the Normal distribution is in question)
you could use the appropriate test-statistic
- z-test
- t-test
- use chi squared distribution
depending on the parameter you test and your sample
I hope that this is of some help.
Thank you Zoran Maksimovic , that information helped me a lot actually. Thank you very much!
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