Nonlinear Wasserstein Distributionally Robust Optimal Control

TL;DR

This paper introduces a dynamic Wasserstein distributionally robust control method for nonlinear systems, providing a practical algorithm and theoretical analysis to manage ambiguity propagation in model predictive control.

Contribution

It develops a novel DRNMPC scheme that dynamically controls ambiguity propagation using an iterative linear quadratic regulator, filling a gap in practical algorithms for dynamic settings.

Findings

The proposed algorithm effectively controls Wasserstein ambiguity in simulations.

Theoretical characterization of stochastic error reachable sets under ambiguity.

Improved closed-loop performance demonstrated on a mass-spring system.

Abstract

This paper presents a novel approach to addressing the distributionally robust nonlinear model predictive control (DRNMPC) problem. Current literature primarily focuses on the static Wasserstein distributionally robust optimal control problem with a prespecified ambiguity set of uncertain system states. Although a few studies have tackled the dynamic setting, a practical algorithm remains elusive. To bridge this gap, we introduce an DRNMPC scheme that dynamically controls the propagation of ambiguity, based on the constrained iterative linear quadratic regulator. The theoretical results are also provided to characterize the stochastic error reachable sets under ambiguity. We evaluate the effectiveness of our proposed iterative DRMPC algorithm by comparing the closed-loop performance of feedback and open-loop on a mass-spring system. Finally, we demonstrate in numerical experiments that our algorithm controls the propagated Wasserstein ambiguity.