Step up regulator with fading input
This is a cheap &amp; dirty solution
Some adjustments on Rb are needed depending on LED strip current and hFE of transistor.
Use an NPN on the low side and using voltage-controlled base current with collector amplification to saturation you can get almost the same effect. Using a transistor rated for 10x actual current for best results.
At half power, the transistor dissipates a lot of power so a heat sink might be needed