MHB Linear Quadratic Gaussian (LQG) regulators

Dustinsfl
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How do LQG regulators work?

I have read the Matlab page about them, Wikipedia, and a few schools notes on them but it isn't either clear to me or they are not adequately explaining how they work. All see is that we want to control something giving a quadratic cost.

Is there are more robust way to explain this (greater depth or detail for a better understanding besides control and quadratic cost)?
 
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