A General Framework for Learning-Based Distributionally Robust MPC of Markov Jump Systems

Abstract

We present a novel class of ambiguity sets for distributionally robust optimization (DRO). These ambiguity sets, called cost-aware ambiguity sets, are defined as halfspaces which depend on the cost function evaluated at an independent estimate of the optimal solution, thus excluding only those distributions that are expected to have significant impact on the obtained worst-case cost. We show that the resulting DRO method provides both a high-confidence upper bound and a consistent estimator of the out-of-sample expected cost, and demonstrate empirically that it results in less conservative solutions compared to divergence-based ambiguity sets.

Data-driven distributionally robust iterative risk-constrained model predictive control

“…where Q : X → R gives the minimum cost-to-go for all states in S and is calculated in a similar manner as in (11). The decision variables in the above problem are (x 0 , x 1 , .…”

“…[Informal description of Algorithm 2]: The procedure generates a trajectory from x S to x F given sampled-safe-set S and an ambiguity set D. The minimum cost-to-go function Q is computed for S using (11). At time-step t, problem (13) is solved with x = x t .…”

“…These can be broadly categorized into methods that focus on propagation of ambiguity sets [4], [5], tube-based MPC [6], [8], reformulations and finite-sample guarantees [7], [13], and chance-constraints and data-driven control [9]. In [10], [11], reformulations and guarantees for DR-based MPC are explored while using the connection that the so-called coherent risk measure of a random variable is equivalent to the worst-case expectation over a set of distributions. Similar connection is used to investigate riskaverse MPC for Markovian switched systems in [14], [15] Most of the above-listed works on MPC are focused on stochastic systems, while we consider deterministic systems that operate under uncertain environments.…”

Sim2real for Autonomous Vehicle Control using Executable Digital Twin

“…Moreover, a popular method for adapting the NMPC model, is through residual dynamics learning using neural networks [4] or Gaussian Processes [5]. Adaptation to reduce conservatism compared to robust control as in [6], and safe environment learning [7], are also relevant. However, most of these methods affect the real-time applicability and structure of the NMPC, or require a large amount of data to train offline, or are not suitable for online training as parameter adaptation requires exploiting the domain of available parameters.…”

Joint Detection and Communication over Type-Sensitive Networks

“…The notion of type has a rich history in information theory and statistics, being first introduced by Csiszar [ 17 ]. Today, the method of types has been further developed [ 18 ] and is used in a variety of fields, such as control [ 19 ], machine learning [ 20 ], statistics [ 21 ], and even DNA storage channels [ 22 ].…”