Stochastic Exponential Stability of Nonlinear Stochastic Model Predictive Control

In this work, we define and establish a selection of significant and new properties for nonlinear stochastic model predictive control (SMPC). First, we ensure that the underlying stochastic properties of the closed-loop stochastic system are indeed well-defined. We then define robust exponential stability in expectation (RESiE) and establish that nonlinear SMPC, under suitable assumptions, renders the origin of the closed-loop system RESiE. We conclude with a numerical example to demonstrate the implications of this analysis.