i already have a DAC circuit that can adjust 1-5V of the output, but i try to give the output of DAC as an input of the amplifier, and it's not work properly..
The output of the DAC might be DC. If you amplify it to 12VDC at up to 50W/12V= 4.2A then the amplifier will be linear and get very hot.
Pulse-Width-Modulation pulses should be used instead so that the switching output does not waste power by getting hot.
I do not know an Arduino but I think it can easily produce PWM. A logic-level Mosfet can be the amplifier. The PWM simply switches it on and off. The width of the pulses determines the brightness of the light bulb. Because the Mosfet switches on with almost no voltage across it and switches off with no current in it then its heating (voltage times current) is very low.