I am trying to understand optimal control theory which forms the base for reinforcement learning techniques in AI. Whenever I open a lecture or a book or any online notes, everything starts with an ode and then derivation goes the payoff function which is straight forward.
I am trying hard to comprehend why an ODE models any system ? Many say it easy to begin with but why this model ?
$dx/dt = f(x(t))$
I could not find the reason and decided to ask for help.