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We are motivated by the lack of discussion surrounding methodological controldesign procedures for nonlinear shot and L\'evy noise stochastic systems topropose a hierarchical controller synthesis method with two parts. The firstpart is a primitive pattern-learning component which recognizes specific statesequences and stores in memory the corresponding control action that needs tobe taken when the sequence has occurred. The second part is a modulationcontrol component which computes the optimal control action for a pattern whenit has occurred for the first time. Throughout our presentation of bothcomponents, we provide a self-contained discussion of theoretical concepts fromPoisson processes theory, renewal theory, and impulse control, all of which arenecessary as background. We demonstrate application of this controller to thesimplified, concrete case studies of fault-tolerance and vehicle congestioncontrol.

A Two-Part Controller Synthesis Approach for Nonlinear Stochastic  Systems Perturbed by L\'evy Noise Using Renewal Theory and HJB-Based Impulse  Control