I'm working with embedded systems. For the sake of explanation, I'm working with a dsPIC33EP and a simple serial EEPROM.
Suppose I'm building a controller that uses a linear control scheme (y=mx+b). If the controller needs may different setting It's easy, store the m and the b in EEPROM and retrieve it for the different settings.
Now suppose I want to have different equations for different settings. I would have to pre program all the equations and then have a method for selecting that equation and pulling the settings from the EEPROM. It's harder because you need to know the equations ahead of time but still doable.
Now suppose that you don't know the equations ahead of time. Maybe you have to do a piece wise approximation for example. How could you store something like that in memory? That all a controller has to do is feed it a sensor reading and it would give back a control variable. Kind of like passing a variable to a function and getting the answer passed back.
How could you store a function like that in memory if only the current state is important?
How could you store a function like that if past states are important (if the control equation is second, third or fourth order for example)?
The dsPICs have limited RAM, but quite a bit of FLASH, enough for a small, but effective text parser. Have you thought of using some form of text based script? These can be translated to a more efficient data format at run-time.