You seem to want to use the IR21XX controller, so in order to get some charge in that bootstrap cao at startup, you can put a high value resistor across the buck diode……..that will start it off for you….as long as you wait for the boot cap to get charged before you aply pwm.
But really you want to be using a dedicated buck controller such as the linear.com ones like LT3892 ETC ETC…or any other semico.
Or do a sepic instead.
I don’t see any feedback. If you are regulating the current and not the output voltage into the battery, then it shouldn’t be a problem to regulate it…but if you are trying to regulate the voltage across the battery at full charge, then that can be a problem, as the batt is like a enormous value cap, and so your compensation will need to take that into account……but its not a problem if you are closing the loop round the batt charge current.