Control optimization problem 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.
This looks like it might be able to be written as a dynamic programming problem. Bellman's equation looks very similar to the way you have expressed your control problem.