Optimising an input signal for a system to minimise distortion of output signal
System is non linear so all bets are off.

Jokes aside though, wouldn't you just characterize the system, then generate an inverse system that the signal passes through first such that the effects of the original system are cancelled out?

Edit: another potential solution is to 'linearize' the system by finding the characteristics of it, then scaling your input signal such that the system behaves in a linear way. Then follow the inverse idea that I gave in my original comment.