2022/06/18 by Fan Wu, Wu, Fan, Mario E. Villanueva +3 · 1 citation
Engineering · #Advanced Control Systems Optimization #Control Systems and Identification #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems
paper · pdf · doi:10.48550/arxiv.2206.09085
openalex publication_date 2022/06/18 · openalex created_date 2022/12/14 · openalex updated_date 2026/07/28
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.