Light Transport; Low Wing; 2 Turbojet Eng
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 7
Situational Awareness; Distraction; Workload
ATC Issue All Types; Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued New Clearance; Air Traffic Control Issued Advisory / Alert; Flight Crew Executed Go Around / Missed Approach; Flight Crew Requested ATC Assistance / Clarification
Airspace Structure; Procedure; Human Factors; Chart Or Publication
I was working a sector and Controller in Charge combined during the event. I cleared an aircraft for the approach to maintain 13;000 feet until established on the localizer.  As I was about to switch the aircraft to Tower I noticed that they were at 12;100 feet on the approach.  The crossing altitude at the fix they were cleared to is 12;900 feet so I issued a low altitude alert and the crossing altitude.  The aircraft responded that they did not have the runway in sight and wanted to go around.  Since they were on an instrument approach I told them to execute the missed approach.  I noticed the aircraft continued to descend; so I issued another low altitude alert; this time using the 12;100 foot Minimum Vectoring Altitude as a reference since they were at 11;700 feet and advised they climb to 14;000 feet  immediately. Once the aircraft was above MVAs I issued a heading and eventually notified them of a possible pilot deviation and gave them the tower number.
A TRACON Controller reported an aircraft descended below their assigned altitude and flew below the Minimum Vectoring Altitude.