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A variety of complex biological, natural and man-made systems exhibit non-Markovian dynamics that can be modeled through fractional order differential equations, yet, we lack sample comlexity aware system identification strategies. Towards…
This paper addresses the problem of identifying sparse linear time-invariant (LTI) systems from a single sample trajectory generated by the system dynamics. We introduce a Lasso-like estimator for the parameters of the system, taking into…
In this paper, we study the system identification problem for sparse linear time-invariant systems. We propose a sparsity promoting block-regularized estimator to identify the dynamics of the system with only a limited number of input-state…
The identification of a linear system model from data has wide applications in control theory. The existing work that provides finite sample guarantees for linear system identification typically uses data from a single long system…
We propose Lagrangian Descriptors (LDs) as a diagnostic framework for evaluating neural network models of Hamiltonian systems beyond conventional trajectory-based metrics. Standard error measures quantify short-term predictive accuracy but…
Identification of a linear time-invariant dynamical system from partial observations is a fundamental problem in control theory. Particularly challenging are systems exhibiting long-term memory. A natural question is how learn such systems…
Performance of ordinary least squares(OLS) method for the \emph{estimation of high dimensional stable state transition matrix} $A$(i.e., spectral radius $\rho(A)<1$) from a single noisy observed trajectory of the linear time…
Ordinary Differential Equations are a simple but powerful framework for modeling complex systems. Parameter estimation from times series can be done by Nonlinear Least Squares (or other classical approaches), but this can give…
This paper studies the linear system identification problem in the general case where the disturbance is sub-Gaussian, correlated, and possibly adversarial. First, we consider the case with noncentral (nonzero-mean) disturbances for which…
Given a single trajectory of a dynamical system, we analyze the performance of the nonparametric least squares estimator (LSE). More precisely, we give nonasymptotic expected $l^2$-distance bounds between the LSE and the true regression…
Identifying a linear system model from data has wide applications in control theory. The existing work on finite sample analysis for linear system identification typically uses data from a single system trajectory under i.i.d random inputs,…
This paper investigates a class of non-autonomous highly oscillatory ordinary differential equations characterized by a linear component inversely proportional to a small parameter $\varepsilon$, with purely imaginary eigenvalues, and an…
We describe a method for the identification of models for dynamical systems from observational data. The method is based on the concept of symbolic regression and uses genetic programming to evolve a system of ordinary differential…
For N-dimensional (ND) static quadratic map, we present a time-delay approach to gradient-based extremum seeking (ES) both, in the continuous and, for the first time, the discrete domains. As in the recently introduced (for 2D maps in the…
We consider the problem of least squares parameter estimation from single-trajectory data for discrete-time, unstable, closed-loop nonlinear stochastic systems, with linearly parameterised uncertainty. Assuming a region of the state space…
Ordinary differential equations (ODEs) are widely used to describe the time evolution of natural phenomena across various scientific fields. Estimating the parameters of these systems from data is a challenging task, particularly when…
The performance of Orthogonal Matching Pursuit (OMP) for variable selection is analyzed for random designs. When contrasted with the deterministic case, since the performance is here measured after averaging over the distribution of the…
Modeling dynamical systems is important in many disciplines, e.g., control, robotics, or neurotechnology. Commonly the state of these systems is not directly observed, but only available through noisy and potentially high-dimensional…
In data-driven modeling of spatiotemporal phenomena careful consideration often needs to be made in capturing the dynamics of the high wavenumbers. This problem becomes especially challenging when the system of interest exhibits shocks or…
Ordinary least-squares (OLS) estimators for a linear model are very sensitive to unusual values in the design space or outliers among y values. Even one single atypical value may have a large effect on the parameter estimates. This article…