Ambiguity tube MPC

This paper is about a class of distributionally robust model predictive controllers (MPC) for nonlinear stochastic processes, which 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 using methods from the field of optimal transport theory. Moreover, an analysis technique based on supermartingales is proposed, leading to stochastic stability results for a large class of distributionally robust controllers. 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.