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Predicting the evolution of systems that exhibit spatio-temporal dynamics in response to external stimuli is a key enabling technology fostering scientific innovation. Traditional equations-based approaches leverage first principles to…

The theory of Kazantzis-Kravaris/Luenberger (KKL) observer design introduces a methodology that uses a nonlinear transformation map and its left inverse to estimate the state of a nonlinear system through the introduction of a linear…

Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions…

We consider the problem of controlling a possibly unknown linear dynamical system with adversarial perturbations, adversarially chosen convex loss functions, and partially observed states, known as non-stochastic control. We introduce a…

Established techniques that enable robots to learn from demonstrations are based on learning a stable dynamical system (DS). To increase the robots' resilience to perturbations during tasks that involve static obstacle avoidance, we propose…

We study the global convergence of generative adversarial imitation learning for linear quadratic regulators, which is posed as minimax optimization. To address the challenges arising from non-convex-concave geometry, we analyze the…

This paper studies the linear quadratic regulation (LQR) problem of unknown discrete-time systems via dynamic output feedback learning control. In contrast to the state feedback, the optimality of the dynamic output feedback control for…

The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and…

Efficient estimation of high-dimensional matrices-including covariance and precision matrices-is a cornerstone of modern multivariate statistics. Most existing studies have focused primarily on the theoretical properties of the estimators…

Neural networks are predominantly trained using gradient-based methods, yet in many applications their final predictions remain far from the accuracy attainable within the model's expressive capacity. We introduce Linearized Subspace…

Machine learning methods are commonly used to solve inverse problems, wherein an unknown signal must be estimated from few indirect measurements generated via a known acquisition procedure. In particular, neural networks perform well…

We study the problem of estimating an unknown deterministic signal that is observed through an unknown deterministic data matrix under additive noise. In particular, we present a minimax optimization framework to the least squares problems,…

This paper describes a method for learning low-dimensional approximations of nonlinear dynamical systems, based on neural-network approximations of the underlying Koopman operator. Extended Dynamic Mode Decomposition (EDMD) provides a…

The problem of system identification for the Kalman filter, relying on the expectation-maximization (EM) procedure to learn the underlying parameters of a dynamical system, has largely been studied assuming that observations are sampled at…

Across scientific domains, a fundamental challenge is to characterize and compute the mappings from underlying physical processes to observed signals and measurements. While nonlinear neural networks have achieved considerable success, they…

In this work, we study the problem of learning partially observed linear dynamical systems from a single sample trajectory. A major practical challenge in the existing system identification methods is the undesirable dependency of their…

Normalizing Flows are a promising new class of algorithms for unsupervised learning based on maximum likelihood optimization with change of variables. They offer to learn a factorized component representation for complex nonlinear data and,…

A common pipeline in learning-based control is to iteratively estimate a model of system dynamics, and apply a trajectory optimization algorithm - e.g.~$\mathtt{iLQR}$ - on the learned model to minimize a target cost. This paper conducts a…

Inverse reinforcement learning (IRL) for linear systems seeks a cost function whose optimal controller reproduces an expert policy from data. Existing data-driven methods for discrete-time linear systems are largely built on iterative…

This paper proposes a data-driven control framework to regulate an unknown, stochastic linear dynamical system to the solution of a (stochastic) convex optimization problem. Despite the centrality of this problem, most of the available…