How do I work out the Inductor value on my a digitally controlled conventional boost converter
Part of the circuit as you know, involves a Boost converter. Due to me
  not having a lab available due to the pandemic, I therefore need some
  theoretical guidance in trying to figure this out.


For a DCM boost converter (the type most regularly used): -

Fact 1 – The inductor in a boost converter has to despatch sufficient energy during each switching cycle to keep the load at the desired voltage. 

Fact 2 – The cyclical energy despatched, multiplied by the switching frequency, equals the power required by the load to raise its voltage from the input voltage level to the required output voltage. This is the “power lift”.

An Example: 


Input voltage is 100 volts. 
Desired Output voltage is 150 volts at 0.6 amps. 
\$F_{SWITCH}\$ = 100 kHz


Power and Energy Calculations:


The power uplift is (150 -100) x 0.6 = 30 watts
The energy uplift is 30 watts ÷ \$F_{SWITCH}\$ = 300 µJ


Assume that the input voltage could be as low as 90 volts: -


Raising 90 volts to 150 volts at 0.6 amps is a power uplift of 36 watts.


Inductance calculation:



Boost inductor calculator:



A duty cycle of 25% was chosen in the above to ensure that the circuit didn't slip into CCM (different formulas). With the charge period being 25% of the time and the discharge period being about 37% of the time this leaves a hold-time of about 38% of the cycle (a bit of spare room).

Simulation output:



Simulation circuit: