Astable multivibrator with increasing frequency
One approach would be to use a voltage controlled oscillator (VCO) and a ramp generating circuit.

The CD4046 has a VCO block in it or there are some function generator ics, like the MAX038. You'll need to find something that covers that range of frequency you need. To produce a ramp, it could be as simple as a capacitor pulled up (or down) to the input of the VCO.

If you need a linear ramp, then driving the capacitor with a current source would be more suitable.