I am running into a problem where I have a control system $S[t]$ that takes a control $C[t]$, so that $$S[t+1] = H(C[t,t-1,...], S[t,t-1,...])$$ the response of the system is the history of controls and responses.
I am looking for a way to control $C[t]$ to optimize the value of $S[t]$ at any point in time.
What is the literature on this problem called? Where do I start looking? Thanks.