相关论文: Geometric Data-Driven Dimensionality Reduction in …

We study adaptive data-dependent dimensionality reduction in the context of supervised learning in general metric spaces. Our main statistical contribution is a generalization bound for Lipschitz functions in metric spaces that are…

Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have…

In this paper, we propose a Transformer-based framework for approximating solutions to infinite-dimensional optimization problems: calculus of variations problems and optimal control problems. Our approach leverages offline training on data…

In this paper we introduce an iterative Jacobi algorithm for solving distributed model predictive control (DMPC) problems, with linear coupled dynamics and convex coupled constraints. The algorithm guarantees stability and persistent…

Adaptive model predictive control (MPC) robustly ensures safety while reducing uncertainty during operation. In this paper, a distributed version is proposed to deal with network systems featuring multiple agents and limited communication.…

Moment-based distributionally robust optimization (DRO) provides an optimization framework to integrate statistical information with traditional optimization approaches. Under this framework, one assumes that the underlying joint…

Model predictive control (MPC) solves a receding-horizon optimization problem in real-time, which can be computationally demanding when there are thousands of constraints. To accelerate online computation of MPC, we utilize data to…

Reduced order models are computationally inexpensive approximations that capture the important dynamical characteristics of large, high-fidelity computer models of physical systems. This paper applies machine learning techniques to improve…

Real-world data typically contain repeated and periodic patterns. This suggests that they can be effectively represented and compressed using only a few coefficients of an appropriate basis (e.g., Fourier, Wavelets, etc.). However, distance…

The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…

This work proposes an approach that integrates reinforcement learning and model predictive control (MPC) to solve finite-horizon optimal control problems in mixed-logical dynamical systems efficiently. Optimization-based control of such…

In distributed model predictive control (MPC), the control input at each sampling time is computed by solving a large-scale optimal control problem (OCP) over a finite horizon using distributed algorithms. Typically, such algorithms require…

Dimensionality reduction represents the process of generating a low dimensional representation of high dimensional data. Motivated by the formation control of mobile agents, we propose a nonlinear dynamical system for dimensionality…

We develop a computational framework for D-optimal experimental design for PDE-based Bayesian linear inverse problems with infinite-dimensional parameters. We follow a formulation of the experimental design problem that remains valid in the…

We develop a novel form of differentiable predictive control (DPC) with safety and robustness guarantees based on control barrier functions. DPC is an unsupervised learning-based method for obtaining approximate solutions to explicit model…

Analyzing relationships between objects is a pivotal problem within data science. In this context, Dimensionality reduction (DR) techniques are employed to generate smaller and more manageable data representations. This paper proposes a new…

Distributed model predictive control (DMPC) has attracted extensive attention as it can explicitly handle system constraints and achieve optimal control in a decentralized manner. However, the deployment of DMPC strategies generally…

We introduce a novel data-driven method to mitigate the risk of cascading failures in delayed discrete-time Linear Time-Invariant (LTI) systems. Our approach involves formulating a distributionally robust finite-horizon optimal control…

Dimensionality reduction is a classical technique widely used for data analysis. One foundational instantiation is Principal Component Analysis (PCA), which minimizes the average reconstruction error. In this paper, we introduce the…

In this paper we propose a constrained guaranteed cost robust model predictive controller (GCMPC) for uncertain discrete time systems. This controller was developed based on a quadratic cost functional and guarantee robustness with respect…