Related papers: Bridging direct & indirect data-driven control for…

In recent years, understanding the implicit regularization of neural networks (NNs) has become a central task in deep learning theory. However, implicit regularization is itself not completely defined and well understood. In this work, we…

We study the problem of target stabilization with robust obstacle avoidance in robots and vehicles that have access only to vision-based sensors for the purpose of realtime localization. This problem is particularly challenging due to the…

This paper addresses the problem of optimally controlling nonlinear systems with norm-bounded disturbances and parametric uncertainties while robustly satisfying constraints. The proposed approach jointly optimizes a nominal nonlinear…

This note presents a unified analysis of the identification of dynamical systems with low-rank constraints under high-dimensional scaling. This identification problem for dynamic systems are challenging due to the intrinsic dependency of…

This paper proposes a data-driven motion-planning framework for nonlinear systems that constructs a sequence of overlapping invariant polytopes. Around each randomly sampled waypoint, the algorithm identifies a convex admissible region and…

Efforts to understand the generalization mystery in deep learning have led to the belief that gradient-based optimization induces a form of implicit regularization, a bias towards models of low "complexity." We study the implicit…

In recent years, the success of the Koopman operator in dynamical systems analysis has also fueled the development of Koopman operator-based control frameworks. In order to preserve the relatively low data requirements for an approximation…

Considering discrete-time linear time-varying systems with unknown dynamics, controllers guaranteeing bounded closed-loop trajectories, optimal performance and robustness to process and measurement noise are designed via convex feasibility…

In structured prediction problems where we have indirect supervision of the output, maximum marginal likelihood faces two computational obstacles: non-convexity of the objective and intractability of even a single gradient computation. In…

To address the challenges of reliable statistical inference in high-dimensional models, we introduce the Synthetic-data Regularized Estimator (SRE). Unlike traditional regularization methods, the SRE regularizes the complex target model via…

We consider a class of learning problem of point estimation for modeling high-dimensional nonlinear functions, whose learning dynamics is guided by model training dataset, while the estimated parameter in due course provides an acceptable…

The explicit low-rank regularization, e.g., nuclear norm regularization, has been widely used in imaging sciences. However, it has been found that implicit regularization outperforms explicit ones in various image processing tasks. Another…

We consider the decentralized control of a discrete-time, linear system subject to exogenous disturbances and polyhedral constraints on the state and input trajectories. The underlying system is composed of a finite collection of…

Although Koopman operators provide a global linearization for autonomous dynamical systems, nonautonomous systems are not globally linear in the inputs. State (or output) feedback controller design therefore remains nonconvex in typical…

The subspace method is one of the mainstream system identification method of linear systems, and its basic idea is to estimate the system parameter matrices by projecting them into a subspace related to input and output. However, most of…

We present an extension of Willems' Fundamental Lemma to the class of multi-input multi-output discrete-time feedback linearizable nonlinear systems, thus providing a data-based representation of their input-output trajectories. Two sources…

This survey presents recent research on determining control-theoretic properties and designing controllers with rigorous guarantees using semidefinite programming and for nonlinear systems for which no mathematical models but measured…

Over the past decades, the Koopman operator has been widely applied in data-driven control, yet its theoretical foundations remain underexplored. This paper establishes a unified framework to address the robust stabilization problem in…

From the statistical learning perspective, complexity control via explicit regularization is a necessity for improving the generalization of over-parameterized models. However, the impressive generalization performance of neural networks…

We propose an approach to trajectory optimization for piecewise polynomial systems based on the recently proposed graphs of convex sets framework. We instantiate the framework with a convex relaxation of optimal control based on occupation…