  We are motivated by the lack of discussion surrounding methodological control
design procedures for nonlinear shot and L\'evy noise stochastic systems to
propose a hierarchical controller synthesis method with two parts. The first
part is a primitive pattern-learning component which recognizes specific state
sequences and stores in memory the corresponding control action that needs to
be taken when the sequence has occurred. The second part is a modulation
control component which computes the optimal control action for a pattern when
it has occurred for the first time. Throughout our presentation of both
components, we provide a self-contained discussion of theoretical concepts from
Poisson processes theory, renewal theory, and impulse control, all of which are
necessary as background. We demonstrate application of this controller to the
simplified, concrete case studies of fault-tolerance and vehicle congestion
control.
