Related papers: Kernel Methods for Linear Discrete-Time Equations

This paper discusses discretization methods for implementing nonlinear model predictive controllers using Iterative Linear Quadratic Regulator (ILQR). Finite-difference approximations are mostly used to derive a discrete-time state equation…

In this paper, we study the statistical difficulty of learning to control linear systems. We focus on two standard benchmarks, the sample complexity of stabilization, and the regret of the online learning of the Linear Quadratic Regulator…

This monograph develops a unified, application-driven framework for kernel methods grounded in reproducing kernel Hilbert spaces (RKHS) and optimal transport (OT). Part I lays the theoretical and numerical foundations on positive-definite…

We discuss the role of monotonicity in enabling numerically tractable modular control design for networked nonlinear systems. We first show that the variational systems of monotone systems can be embedded into positive systems. Utilizing…

In this paper, a polynomial chaos based framework for designing controllers for discrete time linear systems with probabilistic parameters is presented. Conditions for exponential-mean-square stability for such systems are derived and…

The prediction of behavior in dynamical systems, is frequently subject to the design of models. When a time series obtained from observing the system is available, the task can be performed by designing the model from these observations…

System stabilization via policy gradient (PG) methods has drawn increasing attention in both control and machine learning communities. In this paper, we study their convergence and sample complexity for stabilizing linear time-invariant…

Through the method of Learning Feedback Linearization, we seek to learn a linearizing controller to simplify the process of controlling a car to race autonomously. A soft actor-critic approach is used to learn a decoupling matrix and drift…

This paper presents a method for learning Hamiltonian dynamics from a limited set of data points. The Hamiltonian vector field is found by regularized optimization over a reproducing kernel Hilbert space of vector fields that are inherently…

We present a sample-based Learning Model Predictive Controller (LMPC) for constrained uncertain linear systems subject to bounded additive disturbances. The proposed controller builds on earlier work on LMPC for deterministic systems.…

This paper presents a unifying theory of Linear second order systems that allows time-varying and time invariant systems to be treated in the same way for the first time. In the process, a transformation is given that diagonalizes an…

Accurately predicting the dynamics of robotic systems is crucial for model-based control and reinforcement learning. The most common way to estimate dynamics is by fitting a one-step ahead prediction model and using it to recursively…

Empirical observation of high dimensional phenomena, such as the double descent behaviour, has attracted a lot of interest in understanding classical techniques such as kernel methods, and their implications to explain generalization…

Using transformers over large generated datasets, we train models to learn mathematical properties of differential systems, such as local stability, behavior at infinity and controllability. We achieve near perfect prediction of qualitative…

We study challenges using reinforcement learning in controlling energy systems, where apart from performance requirements, one has additional safety requirements such as avoiding blackouts. We detail how these safety requirements in…

Under mild assumptions on the kernel, we obtain the best known error rates in a regularized learning scenario taking place in the corresponding reproducing kernel Hilbert space (RKHS). The main novelty in the analysis is a proof that one…

Metrics specifying distances between data points can be learned in a discriminative manner or from generative models. In this paper, we show how to unify generative and discriminative learning of metrics via a kernel learning framework.…

Many modern datasets don't fit neatly into $n \times p$ matrices, but most techniques for measuring statistical stability expect rectangular data. We study methods for stability assessment on non-rectangular data, using statistical learning…

Incorporating a priori physics knowledge into machine learning leads to more robust and interpretable algorithms. In this work, we combine deep learning techniques and classic numerical methods for differential equations to address two…

We present an integrated approach for the use of simulated data from full order discretization as well as projection-based Reduced Basis reduced order models for the training of machine learning approaches, in particular Kernel Methods, in…