Safe Zero-Shot Model-Based Learning and Control: A Wasserstein Distributionally Robust Approach

This paper explores distributionally robust zero-shot model-based learning and control using Wasserstein ambiguity sets. Conventional model-based reinforcement learning algorithms struggle to guarantee feasibility throughout the online learning process. We address this open challenge with the following approach. Using a stochastic model-predictive control (MPC) strategy, we augment safety constraints with affine random variables corresponding to the instantaneous empirical distributions of modeling error. We obtain these distributions by evaluating model residuals in real time throughout the online learning process. By optimizing over the worst case modeling error distribution defined within a Wasserstein ambiguity set centered about our empirical distributions, we can approach the nominal constraint boundary in a provably safe way. We validate the performance of our approach using a case study of lithium-ion battery fast charging, a relevant and safety-critical energy systems control application. Our results demonstrate marked improvements in safety compared to a basic learning model-predictive controller, with constraints satisfied at every instance during online learning and control.Comment: In review for CDC2

A Mixed-Integer SDP Solution Approach to Distributionally Robust Unit Commitment with Second Order Moment Constraints

A power system unit commitment (UC) problem considering uncertainties of renewable energy sources is investigated in this paper, through a distributionally robust optimization approach. We assume that the first and second order moments of stochastic parameters can be inferred from historical data, and then employed to model the set of probability distributions. The resulting problem is a two-stage distributionally robust unit commitment with second order moment constraints, and we show that it can be recast as a mixed-integer semidefinite programming (MI-SDP) with finite constraints. The solution algorithm of the problem comprises solving a series of relaxed MI-SDPs and a subroutine of feasibility checking and vertex generation. Based on the verification of strong duality of the semidefinite programming (SDP) problems, we propose a cutting plane algorithm for solving the MI-SDPs; we also introduce a SDP relaxation for the feasibility checking problem, which is an intractable biconvex optimization. Experimental results on a IEEE 6-bus system are presented, showing that without any tunings of parameters, the real-time operation cost of distributionally robust UC method outperforms those of deterministic UC and two-stage robust UC methods in general, and our method also enjoys higher reliability of dispatch operation

Distributionally Robust Optimization Techniques for Stochastic Optimal Control

Distributionally robust optimal control is a relatively new field of robust control that tries to address the issue of safety by hedging against the worst-cast distributions. However, because probability distributions are infinite-dimensional, this problem is in general computationally intractable. This thesis provides an overview of applications of distributionally robust optimization for stochastic optimal control. In particular, we look at existing and potentially new computationally tractable methods for performing distributionally robust optimal control using the Wasserstein metric.Undergraduat