Volterra series

About: Volterra series is a research topic. Over the lifetime, 2731 publications have been published within this topic receiving 46199 citations.

Nonparametric volterra kernel estimation using regularization

Abstract: Modeling of nonlinear dynamic systems constitutes one of the most challenging topics in the field of system identifi- cation. One way to describe the nonlinear behavior of a process is by use of the nonparametric Volterra Series representation. The drawback of this method lies in the fact that the number of parameters to be estimated increases fast with the number of lags considered for the description of the several impulse responses. The result is that the estimated parameters admit a very large variance leading to a very uncertain description of the nonlinear system. In this paper, inspired from the regularization techniques that have been applied to one-dimensional (1-D) impulse responses for a linear time invariant (LTI) system, we present a method to estimate efficiently finite Volterra kernels. The latter is achieved by constraining the estimated parameters appropriately during the identification step in a way that prior knowledge about the to-be-estimated kernels is reflected on the resulting model. The enormous benefit for the identification of Volterra kernels due to the regularization is illustrated with a numerical example.

Nonlinear identification and robust tracking control of a camless engine valve actuator based on a Volterra series representation

Abstract: This paper presents the nonlinear identification and the robust position tracking control of a camless engine valve actuator in frequency domain. If a periodic signal excites a nonlinear system, it turns out to generate output spectrum at multiple harmonic frequencies other than that of the excitation. Therefore, such nonlinear features should be taken account in tracking control system design to improve tracking performance. First, nonlinear identification with a Volterra series representation is proposed to capture nonlinearities. Then, robust tracking control of an uncertain Volterra system based on the internal model principle is addressed. It argues that an internal model unit should embed the extended generating dynamics to suppress tracking error occurring at multiple harmonics. To validate the control design method, the tracking results of two different generating dynamics are compared. From the comparison, tracking performance advances through the extended generating dynamics.

Wiener G-functionals for nonlinear power amplifier digital predistortion

Abstract: This paper expounds on the pruning of Volterra series used to linearize power amplifiers (PAs) exhibiting memory effects. This pruning approach starts with the identification of the minimum set of dominant kernels needed in the Volterra series modeling for a given PA. The pruned Volterra series is then applied to synthesize a digital predistortion (DPD) function. The proposed pruned Volterra series DPD achieved more than 50 dBc ACPR and −38 dB EVM when a 45 Watts GaN PA at 2.14 GHz was driven by a 20 MHz WCDMA signal. In addition, the proposed model was found to lead to reduced span of the kernels values and better numerical conditioning.

Formula for output autocorrelation and spectrum of a Volterra system with stationary Gaussian input

Abstract: It is shown how the output autocorrelation and spectrum of a time-invariant Volterra system with stationary Gaussian input can conveniently be found by converting the Volterra series into a Hermite functional series and then making use of the orthogonality property. The paper extends previous work by the author to derive the well-known formula of Bedrosian-Rice.

A new convergence criteria of volterra series for harmonic inputs

Abstract: The use of Volterra series is often limited by its convergence radius. We will study in this paper a procedure to estimate a majorant of this convergence radius. The criterion which will be developed here is associated to a sinusoidal input and to the first order frequency response of a non-linear system. In order to establish out criterion, the dynamical equations will be re-written by means of the harmonic balance method to estimate the frequency response. The Volterra series obtained with this equation has a convergence radius which can be calculated with the complex variable theory. We will show that the estimation error due to the harmonic balance method does not, change the estimation of the convergence domain. To illustrate out results, we will apply out criterion to a Duffing oscillator and to a two degrees of freedom system with a non linear spring.