Related papers: Kernel-based multi-step predictors for data-driven…
Traditional linear methods for forecasting multivariate time series are not able to satisfactorily model the non-linear dependencies that may exist in non-Gaussian series. We build on the theory of learning vector-valued functions in the…
In this paper, a class of high order numerical schemes is proposed to solve the nonlinear parabolic equations with variable coefficients. This method is based on our previous work [10] for convection-diffusion equations, which relies on a…
This note aims to provide a systematic investigation of direct data-driven control, enriching the existing literature not by adding another isolated result, but rather by offering a unifying, versatile, and broad framework that enables the…
The robotic systems continuously interact with complex dynamical systems in the physical world. Reliable predictions of spatiotemporal evolution of these dynamical systems, with limited knowledge of system dynamics, are crucial for…
The kernel method is a potential approach to analyzing structured data such as sequences, trees, and graphs; however, unordered trees have not been investigated extensively. Kimura et al. (2011) proposed a kernel function for unordered…
Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…
Mathematical modeling is an essential step, for example, to analyze the transient behavior of a dynamical process and to perform engineering studies such as optimization and control. With the help of first-principles and expert knowledge, a…
Safe control for dynamical systems is critical, yet the presence of unknown dynamics poses significant challenges. In this paper, we present a learning-based control approach for tracking control of a class of high-order systems, operating…
This paper presents a new robust data-driven predictive control scheme for unknown linear time-invariant systems by using input-state-output or input-output data based on whether the state is measurable. To remove the need for the…
This paper proposes a data-driven framework to solve time-varying optimization problems associated with unknown linear dynamical systems. Making online control decisions to regulate a dynamical system to the solution of an optimization…
We consider the problem of high-dimensional non-linear variable selection for supervised learning. Our approach is based on performing linear selection among exponentially many appropriately defined positive definite kernels that…
Data-driven control algorithms use observations of system dynamics to construct an implicit model for the purpose of control. However, in practice, data-driven techniques often require excessive sample sizes, which may be infeasible in…
This paper addresses the offset-free tracking problem for nonlinear systems described by a class of recurrent neural networks (RNNs). To compensate for constant disturbances and guarantee offset-free tracking in the presence of model-plant…
We introduce a method to deal with the data-driven control design of nonlinear systems. We derive conditions to design controllers via (approximate) nonlinearity cancellation. These conditions take the compact form of data-dependent…
The derivation of multi-step-ahead prediction models from sampled data of a linear system is considered. A dedicated prediction model is built for each future time step of interest. In addition to a nominal model, the set of all models…
We establish a time-stepping learning algorithm and apply it to predict the solution of the partial differential equation of motion in micromagnetism as a dynamical system depending on the external field as parameter. The data-driven…
Efficient tools for predicting the drag of rough walls in turbulent flows would have a tremendous impact. However, methods for drag prediction rely on experiments or numerical simulations which are costly and time-consuming. Data-driven…
We design specific neural networks (NNs) for the identification of switching nonlinear systems in the state-space form, which explicitly model the switching behavior and address the inherent coupling between system parameters and switching…
Non-parametric representations of dynamical systems based on the image of a Hankel matrix of data are extensively used for data-driven control. However, if samples of data are missing, obtaining such representations becomes a difficult…
A kernel-based framework for spatio-temporal data analysis is introduced that applies in situations when the underlying system dynamics are governed by a dynamic equation. The key ingredient is a representer theorem that involves…