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An effective modeling method for nonlinear distributed parameter systems (DPSs) is critical for both physical system analysis and industrial engineering. In this Rapid Communication, we propose a novel DPS modeling approach, in which a…

Compressive sensing (CS) has recently emerged as a framework for efficiently capturing signals that are sparse or compressible in an appropriate basis. While often motivated as an alternative to Nyquist-rate sampling, there remains a gap…

We introduce Coarse-Grained Nonlinear Dynamics, an efficient and universal parameterization of nonlinear system dynamics based on the Volterra series expansion. These models require a number of parameters only quasilinear in the system's…

In the present paper, two existing nonlinear system identification methodologies are used to identify data-driven models. The first methodology focuses on identifying the system using steady-state excitations. To accomplish this, a…

The discrete prolate spheroidal sequences (DPSS's) provide an efficient representation for discrete signals that are perfectly timelimited and nearly bandlimited. Due to the high computational complexity of projecting onto the DPSS basis -…

Volterra series representation is a powerful mathematical model for nonlinear circuits. However, the difficulties in determining higher-order Volterra kernels limited its broader applications. In this work, a systematic approach that…

Many signal processing problems--such as analysis, compression, denoising, and reconstruction--can be facilitated by expressing the signal as a linear combination of atoms from a well-chosen dictionary. In this paper, we study possible…

This paper considers the design of robust state observers for a class of slope-restricted nonlinear descriptor systems with unknown time-varying parameters belonging to a known set. The proposed design accounts for process disturbances and…

Traditional system identification with multisine inputs relies on uniform sampling and periodic excitation to preserve Fourier orthogonality and avoid spectral leakage, limiting its use in scenarios with irregular sampling or nonperiodic…

Exceptional point degeneracies (EPD) of linear non-Hermitian systems have been recently utilized for hypersensitive sensing. This proposal exploits the sublinear response that the degenerate frequencies experience once the system is…

We propose a class of spectral singularities that are sensitive to the direction of excitation and are arising in nonlinear systems with broken parity symmetry. These spectral singularities are sensitive to the direction of the incident…

Many real world systems exhibit a quasi linear or weakly nonlinear behavior during normal operation, and a hard saturation effect for high peaks of the input signal. In this paper, a methodology to identify a parsimonious discrete-time…

An analysis of discrete systems is important for understanding of various physical processes, such as excitations in crystal lattices and molecular chains, the light propagation in waveguide arrays, and the dynamics of Bose-condensate…

The aim of this work is to investigate the use of Incrementally Input-to-State Stable ($\delta$ISS) deep Long Short Term Memory networks (LSTMs) for the identification of nonlinear dynamical systems. We show that suitable sufficient…

We introduce a nonlinear extension of the joint spectral radius (JSR) for switched discrete-time dynamical systems governed by sub-homogeneous and order-preserving maps acting on cones. We show that this nonlinear JSR characterizes both the…

Spatiotemporal nonlinear interactions in multimode fibers are of interest for beam shaping and frequency conversion by exploiting the nonlinear propagation of different pump regimes from quasi-continuous wave to ultrashort pulses centered…

This paper leverages recent advances in high derivatives reconstruction from noisy-time series and sparse multivariate polynomial identification in order to improve the process of parsimoniously identifying, from a small amount of data,…

In this short paper, we aim at developing algorithms for sparse Volterra system identification when the system to be identified has infinite impulse response. Assuming that the impulse response is represented as a sum of exponentials and…

This paper considers a single-trajectory system identification problem for linear systems under general nonlinear and/or time-varying policies with i.i.d. random excitation noises. The problem is motivated by safe learning-based control for…

This paper introduces a multiple-input discrete Urysohn operator for modelling non-linear control systems and a technique of its identification by processing the observed input and output signals. It is shown that, due to the nature of the…