Yes, the bottom two MOSFETs are to be switched on and off simultaneously. Frequency is up to you. Duty cycle will determine voltage. Think of it as a boost converter. So, Vo = Vi/(1-D), Vo- Output voltage, Vi- Input voltage, D - Duty cycle. Then, consider the losses and voltage drops.
The algorithm could be:
Check battery voltage. If <13.5V (adjust as required), start PWM. Keep on increasing duty cycle until required charging current is passing. Check battery voltage and duty cycle and increase duty cycle if charging current is to be increased and decrease duty cycle if charging current is to be decreased.
Check battery voltage. If >= 13.5V (adjust as required), either stop PWM, or lower charging current (depending on you).
Hope this helps.
Tahmid.