Presume that the voltage waveforms are not showing the real supply voltage but the voltage that arrive at oscilloscope input, measured voltage + common mode noise. It may even be that oscilloscope ground connection is the final reason for controller reset.
The increasing noise level in the waveform suggests a state change in your inverter, e.g. rising output current. There's obviously a problem of inverter switching current/voltage coupling into your control circuit or at least the measurement setup.
I agree with previous contributors that we need to look at schematic and layout details to understand possible coupling pathes.