Related papers: Nonlinear system modeling based on constrained Vol…
This work proposes a low complexity nonlinearity model and develops adaptive algorithms over it. The model is based on the decomposable---or rank-one, in tensor language---Volterra kernels. It may also be described as a product of FIR…
In this paper, the regularization approach introduced recently for nonparametric estimation of linear systems is extended to the estimation of nonlinear systems modelled as Volterra series. The kernels of order higher than one, representing…
The Volterra Tensor Network lifts the curse of dimensionality for truncated, discrete times Volterra models, enabling scalable representation of highly nonlinear system. This scalability comes at the cost of introducing randomness through…
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…
We propose a new algorithm to identify a Wiener-Hammerstein system. This model represents a communication channel where two linear filters are separated by a non-linear function modelling an amplifier. The algorithm enables to recover each…
This paper presents detailed insights of embedding Carleman linearization into nonlinear systems for designing Volterra model-based control technique. Volterra series method is a competent mathematical tool, which extends the convolution…
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…
A novel adaptive filtering method called $q$-Volterra least mean square ($q$-VLMS) is presented in this paper. The $q$-VLMS is a nonlinear extension of conventional LMS and it is based on Jackson's derivative also known as $q$-calculus. In…
There have been increasing interests on the Volterra series identification with the kernel-based regularization method. The major difficulties are on the kernel design and efficiency of the corresponding implementation. In this paper, we…
Providing flexibility and user-interpretability in nonlinear system identification can be achieved by means of block-oriented methods. One of such block-oriented system structures is the parallel Wiener-Hammerstein system, which is a sum of…
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…
The Volterra series can be used to model a large subset of nonlinear, dynamic systems. A major drawback is the number of coefficients required model such systems. In order to reduce the number of required coefficients, Laguerre polynomials…
The implementation of optimal statistical inference protocols for high-dimensional quantum systems is often computationally expensive. To avoid the difficulties associated with optimal techniques, here I propose an alternative approach to…
Nonlinear adaptive filtering allows for modeling of some additional aspects of a general system and usually relies on highly complex algorithms, such as those based on the Volterra series. Through the use of the Kronecker product and some…
Quantum input-output theory plays a very important role for analyzing the dynamics of quantum systems, especially large-scale quantum networks. As an extension of the input-output formalism of Gardiner and Collet, we develop a new approach…
The Volterra integral-functional series is the classic approach for nonlinear black box dynamical systems modeling. It is widely employed in many domains including radiophysics, aerodynamics, electronic and electrical engineering and many…
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…
This paper introduces a method for the nonparametric Bayesian learning of nonlinear operators, through the use of the Volterra series with kernels represented using Gaussian processes (GPs), which we term the nonparametric Volterra kernels…
This paper introduces a novel approach to system identification for nonlinear input-output models that minimizes the simulation error and frames the problem as a constrained optimization task. The proposed method addresses vanishing…
This article introduces two Tensor Network-based iterative algorithms for the identification of high-order discrete-time nonlinear multiple-input multiple-output (MIMO) Volterra systems. The system identification problem is rewritten in…