response of algorithm in non-equidistant time
I would try to stick with a conventional discrete time control approach.  Trying to deal with missing samples in the control algorithm complicates things and without dealing with them the control output will not be very stable.  Can something like this work in your application?

Here the assumption is that you can detect missing samples and use an interpolation algorithm to fill in the gaps before applying the signal to your controller/compensator.  The "Control Signal" input is a reference that can be used to set the normal operating intensity of the Light Source.

I would characterize the transfer function with using normal control signals (impulse, step, swept sine, all with uniform sampling).  Then I would model the real signal (from the lamp transducer) with some impulse variations that match the characteristics of your missing samples.  By impulse variations I mean adding small error quatities to signal to represent error from your interpolator.  Test how well the transfer function regulates in the presense of this "impulse noise".