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This paper examines the problem of stabilizing linear distributed delay systems with nonlinear distributed delay kernels and dissipativity constraints. Specifically, the nonlinear distributed kernel includes functions such as polynomials,…

This paper discusses the solution of nonlinear integral equations with noisy integral kernels as they appear in nonparametric instrumental regression. We propose a regularized Newton-type iteration and establish convergence and convergence…

Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…

This paper proposes a novel kernel-based optimization scheme to handle tasks in the analysis, e.g., signal spectral estimation and single-channel source separation of 1D non-stationary oscillatory data. The key insight of our optimization…

This paper focuses on the system identification of an important class of nonlinear systems: linearly parameterized nonlinear systems, which enjoys wide applications in robotics and other mechanical systems. We consider two system…

Increasing amounts of data are available on temporal, or time-varying, networks. There have been various representations of temporal network data each of which has different advantages for downstream tasks such as mathematical analysis,…

It is well known that the minimax rates of convergence of nonparametric density and regression function estimation of a random variable measured with error is much slower than the rate in the error free case. Surprisingly, we show that if…

We consider the problem of detecting and quantifying the periodic component of a function given noise-corrupted observations of a limited number of input/output tuples. Our approach is based on Gaussian process regression which provides a…

This is a technical report that extends and clarifies the results presented in [1]. The model identification problem for asymptotically stable linear time invariant systems is considered. The system output is affected by an additive noise…

Learning kinetic systems from data is one of the core challenges in many fields. Identifying stable models is essential for the generalization capabilities of data-driven inference. We introduce a computationally efficient framework, called…

We explore extended B-splines as a stable basis for isogeometric analysis with trimmed parameter spaces. The stabilization is accomplished by an appropriate substitution of B-splines that may lead to ill-conditioned system matrices. The…

Identifying parameters in a system of nonlinear, ordinary differential equations is vital for designing a robust controller. However, if the system is stochastic in its nature or if only noisy measurements are available, standard…

The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…

Stabilization of non-stationary linear systems over noisy communication channels is considered. Stochastically stable sources, and unstable but noise-free or bounded-noise systems have been extensively studied in information theory and…

This paper introduces new techniques for using convex optimization to fit input-output data to a class of stable nonlinear dynamical models. We present an algorithm that guarantees consistent estimates of models in this class when a small…

This paper addresses the problem of learning linear dynamical systems from noisy observations. In this setting, existing algorithms either yield biased parameter estimates or have large sample complexities. We resolve these issues by…

Kernels are efficient in representing nonlocal dependence and they are widely used to design operators between function spaces. Thus, learning kernels in operators from data is an inverse problem of general interest. Due to the nonlocal…

Bayesian model updating based on Gaussian Process (GP) models has received attention in recent years, which incorporates kernel-based GPs to provide enhanced fidelity response predictions. Although most kernel functions provide high fitting…

This paper proposes a novel framework for the approximation and analysis of circular density data using compositional periodic splines within Bayes spaces with the Hilbert space structure. By applying the centered log-ratio transformation,…

In this paper, we prove the nonlinear stability under localized perturbations of spectrally stable time-periodic source defects of reaction-diffusion systems. Consisting of a core that emits periodic wave trains to each side, source defects…