Ambiguity Tube MPC

TL;DR

This paper introduces a novel distributionally robust MPC framework for nonlinear stochastic systems using measure-theoretic methods, providing stability analysis and practical design guidelines.

Contribution

It presents a new ambiguity tube MPC formulation based on optimal transport theory and supermartingale analysis for stability in nonlinear stochastic systems.

Findings

Framework ensures stochastic stability for nonlinear systems.

Constructs terminal costs guaranteeing convergence to invariant sets.

Demonstrates effectiveness through examples and a case study.

Abstract

This paper is about a class of distributionally robust model predictive controllers (MPC) for nonlinear stochastic processes that evaluate risk and control performance measures by propagating ambiguity sets in the space of state probability measures. A framework for formulating such ambiguity tube MPC controllers is presented, which is based on modern measure-theoretic methods from the field of optimal transport theory. Moreover, a supermartingale based analysis technique is proposed, leading to stochastic stability results for a large class of distributionally robust controllers for linear and nonlinear systems. In this context, we also discuss how to construct terminal cost functions for stochastic and distributionally robust MPC that ensure closed-loop stability and asymptotic convergence to robust invariant sets. The corresponding theoretical developments are illustrated by tutorial-style examples and a numerical case study.