Stability and performance of stochastic predictive control

TL;DR

This paper investigates the stability and performance of stochastic systems controlled by receding horizon policies, providing methods to ensure stability through cost function design and quantifying long-term performance bounds.

Contribution

It offers a systematic approach to guarantee stability and derive performance bounds for stochastic systems under receding horizon control.

Findings

Stability can be achieved by appropriate cost function selection.

Quantitative bounds on long-term average cost are established.

Illustrative examples demonstrate the theoretical results.

Abstract

This article is concerned with stability and performance of controlled stochastic processes under receding horizon policies. We carry out a systematic study of methods to guarantee stability under receding horizon policies via appropriate selections of cost functions in the underlying finite-horizon optimal control problem. We also obtain quantitative bounds on the performance of the system under receding horizon policies as measured by the long-run expected average cost. The results are illustrated with the help of several simple examples.