Stochastic Model Predictive Control, Iterated Function Systems, and Stability

Abstract: We present the observation that the process of stochastic model predictive control can be formulated in the framework of iterated function systems. The latter has a rich ergodic theory that can be applied to study the system's long-run behavior. We show how such a framework can be realized for specific problems and illustrate the required conditions for the application of relevant theoretical guarantees.