Multiple voltages from a single adapter - 20V ~/200mA, 11V ~/800mA

I have some equipment that uses a voltage power adapter that has the following rating:

Input: 120V ~/60 Hz /120mA /14W
Output: 20V ~/200mA
11V ~/800mA

This equipment was procured from U.S and so the power adapter requires a 120V input. I use a voltage converter to convert my mains voltage from 220v to 120v, and I am able to use the device properly.

But I face a problem when there is a power cut and my mains start running off the house's inverter/UPS. The device keeps restarting on and off, as if there was not enough current being supplied. This has happened not just in my house, but also in a couple of different places.

So I wanted to make a portable battery pack (replacing the existing power adapter) that would give the device power supply that it needs. My main reason for confusion is that the power adapter is providing two different voltages/currents to the device (as per the adapter rating). The adapter plug is ps/2 (like a mouse plug, its got 4 pins, so 2 of them must be ground or something).

I need to understand more about the dual voltage output:
Output: 20V ~/200mA
11V ~/800mA

Can someone help me out with this?

Thanks a lot.