Nonlinear Wasserstein distributionally robust optimal control

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

The Cost of Ambiguity and Robustness in International Pollution Control

This paper examines robustness in international pollution control emerg- ing from the regulator��s concerns regarding possible misspeci��cation of the natural system that is used to model pollution dynamics. Cooperative and noncooperative robust policy rules are determined along with the cost in terms of value loss of being robust relative to conventional policy rules.Ambiguity, Robustness, Precaution, Di¤erential games, Open Loop and Feedback Nash equilibrium