I worked on design of such converters using UC1875 in one design and then DSP control in another. The technique is described in literature (app notes) of the UC1875.
So basically if initially M1 and M4 are conducting and transferring, the M4 is switched off, the M4 drain resonates due to C and Lleakage to the top rail due to being clamped by M3 diode and of course M3 is turned on with lossless zero voltage switched transition. M1 is turned off with zero voltage switching (drain and source at Vin, approximately ). M1 switch capacitance (btw:no addition capacitance is drawn on drawing) provides current path and current still flowing charges M1 switch capacitance to Vin, so M2 drain now is at near zero volts and M2 body diode clamps to diode drop below low rail. With this M2 (zvs) is turned on for power transfer.
Based on those principles appropriate switch control signals can be developed.