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Robust Model Predictive Control (MPC) for nonlinear systems is a problem that poses significant challenges as highlighted by the diversity of approaches proposed in the last decades. Often compromises with respect to computational load,…
This paper is concerned with personalized pricing models aimed at maximizing the expected revenues or profits for a single item. While it is essential for personalized pricing to predict the purchase probabilities for each consumer, these…
Robust Principal Component Analysis (PCA) (Candes et al., 2011) and low-rank matrix completion (Recht et al., 2010) are extensions of PCA to allow for outliers and missing entries respectively. It is well-known that solving these problems…
In this paper we studied combinatorial problems with parameterized locally budgeted uncertainty. We are looking for a solutions set such that for any parameters vector there exists a solution in the set with robustness near optimal. The…
This paper studies the robust optimal control design for uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (robust-ADP). The objective is to fill up a gap in the past literature of ADP where dynamic…
In this paper, we develop a unified framework for studying constrained robust optimal control problems with adjustable uncertainty sets. In contrast to standard constrained robust optimal control problems with known uncertainty sets, we…
This paper introduces an uncertainty compensation-based robust adaptive model predictive control (MPC) framework for linear systems with nonlinear time-varying uncertainties. The framework integrates an L1 adaptive controller to compensate…
Converse optimality theory addresses an optimal control problem conversely where the system is unknown and the value function is chosen. Previous work treated this problem both in continuous and discrete time and non-extensively considered…
Robots must satisfy safety-critical state and input constraints despite disturbances and model mismatch. We introduce a robust model predictive control (RMPC) formulation that is fast, scalable, and compatible with real-time implementation.…
In practical optimization problems, we typically model uncertainty as a random variable though its true probability distribution is unobservable to the decision maker. Historical data provides some information of this distribution that we…
Robust Optimization has traditionally taken a pessimistic, or worst-case viewpoint of uncertainty which is motivated by a desire to find sets of optimal policies that maintain feasibility under a variety of operating conditions. In this…
Based on smoothing techniques, we propose two new methods to solve linear complementarity problems (LCP) called TLCP and Soft-Max. The idea of these two new methods takes inspiration from interior-point methods in optimization. The…
In this paper, we consider the robust linear infinite programming problem $({\rm RLIP}_c) $ defined by \begin{eqnarray*} ({\rm RLIP}_c)\quad &&\inf\; \langle c,x\rangle \textrm{subject to } &&x\in X,\; \langle x^\ast,x \rangle \le r…
A robust model predictive control (MPC) method is presented for linear, time-invariant systems affected by bounded additive disturbances. The main contribution is the offline design of a disturbance-affine feedback gain whereby the…
This work studies the design of safe control policies for large-scale non-linear systems operating in uncertain environments. In such a case, the robust control framework is a principled approach to safety that aims to maximize the…
This paper investigates the problem of robust model predictive control (RMPC) of linear-time-invariant (LTI) discrete-time systems subject to structured uncertainty and bounded disturbances. Typically, the constrained RMPC problem with…
Sliding cable system with frictions is encountered in many engineering applications. Such system is typically characterized by existences of complex and varied motion states of different sliding nodes (pulleys), which leads to significant…
In this work, we propose a robust framework that employs adversarially robust training to safeguard the ML models against perturbed testing data. Our contributions can be seen from both computational and statistical perspectives. Firstly,…
This paper presents an uncertainty compensation-based robust adaptive model predictive control (MPC) framework for linear systems with both matched and unmatched nonlinear uncertainties subject to both state and input constraints. In…
This work proposes a novel robust model predictive control (MPC) algorithm for linear systems affected by dynamic model uncertainty and exogenous disturbances. The uncertainty is modeled using a linear fractional perturbation structure with…