Stochastic Model Predictive Control, Iterated Function Systems, and Stability

TL;DR

This paper links stochastic model predictive control to iterated function systems, leveraging ergodic theory to analyze long-term stability and behavior of controlled stochastic processes.

Contribution

It introduces a novel framework connecting stochastic MPC with iterated function systems, enabling new stability analysis methods.

Findings

Framework applicable to specific control problems

Conditions for theoretical guarantees established

Long-term behavior can be characterized using ergodic theory

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.