Role of Power Metric and LPF in AGC(Automatic Gain Controller)
Either power or rms value is typically used for AGC as a peak value would be much more variable given it is an instantaneous measurement. The low pass filter typically refers to the Loop Filter (and if so, would be better described as such as it more typically done as an integrator) which is a core part of the control loop design. A band pass filter prior to the power detector is also important since any signals within the bandwidth of the filter/detector would control the AGC level. 

Below are example block diagrams depicting typical AGC implementations in the analog and digital domain.  The log and alog interfaces for the digital implementation provide consistent loop bandwidth over the operational range of the AGC due to using multipliers for the gain adjust. 





Further AGC considerations for digital implementation are covered in this post: How to adjust receiver gains to avoid saturation and quantization noise to optimise post digital processing?