As known, the HJB equation is
$-\frac{\partial v}{\partial t}(t,x) - \underset{a\in A}{sup}[L^av(t,x)+f(t,x,a)]=0$ , $ \forall (t,x) \in[0,T)\times R^n$
I understand that $v$ is the value function that we want to evaluate at the optimal control and $L^a$ is the infinitesimal operator that operates on value function. But what is $f(t,x,a)$ here ? Could someone help on this, please?