Volterra series

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

Fundamentals of nonlinear behavioral modeling for RF and microwave design

Abstract: Introduction to Behavioral Modeling. Behavioral Modeling from the Perspective of Nonlinear Dynamics: Time Domain Techniques. Introduction to Volterra Series Analysis. Frequency Domain Methods for Behavioral Modeling. Mixed Time and Frequency Domain Behavioral Modeling and Simulation. Scattering Functions for Nonlinear Behavioral Modeling. Behavioral Modeling with Artificial Neural Networks.

Algebraic and Geometric Methods in Nonlinear Control Theory

Abstract: Controllability, Observability, Realization and other Structural Properties- Realization Theory for Nonlinear Systems Three Approaches- The Local Realization of Generating Series of Finite Lie Rank- Realizations of Polynomial Systems- Symmetries and Local Controllability- The Intrinsic Geometry of Dynamic Observations- Design of Nonlinear Observers by a Two-Step-Transformation- Feedback Synthesis and Linearization Techniques- On the Input-Output Decoupling of Nonlinear Systems- Control of Nonlinear Systems Via Dynamic State-Feedback- A Classification of Nonlinear Systems Based on the Invariant Subdistribution Algorithm- Asymptotic Expansions, Root-Loci and the Global Stability of Nonlinear Feedback Systems- Everything You Always Wanted to Know About Linearization- Feedback Linearization and Simultaneous Output Block Decoupling of Nonlinear Systems- Global Feedback Linearizability of Locally Linearizable Systems- Global Aspects of Linearization, Equivalence to Polynomial Forms and Decomposition of Nonlinear Control Systems- The Extended-Linearization Approach for Nonlinear Systems Problems- About the Local Linearization of Nonlinear Systems- Optimal Control- Envelopes, Conjugate Points, and Optimal Bang-Bang Extremals- Geometry of the Optimal Control- Volterra Series and Optimal Control- Optimal Control and Hamiltonian Input-Output Systems- Discrete-Time Systems- Nonlinear Systems in Discrete Time- Local Input-Output Decoupling of Discrete Time Nonlinear Systems- Orbit Theorems and Sampling- Various other Theoretical Aspects- An Infinite Dimensional Variational Problem Arising in Estimation Theory- Iterated Stochastic Integrals in Nonlinear Control Theory- Approximation of Nonlinear Systems by Bilinear Ones- Applications- Feedback Linearization Techniques in Robotics and Power Systems- CAD for Nonlinear Systems Decoupling, Perturbations Rejection and Feedback Linearization with Applications to the Dynamic Control of a Robot Arm- A Nonlinear Feedback Control Law for Attitude Control- Identification of Different Discrete Models of Continuous Non-linear Systems Application to Two Industrial Pilot Plants- Bang-Bang Solutions for a Class of Problems Arising in Thermal Control

A New Approach to Pruning Volterra Models for Power Amplifiers

Abstract: The objective of this paper is to present an approach to behavioral modeling that can be applied to predict the nonlinear response of power amplifiers with memory. Starting with the discrete-time, complex-baseband full Volterra model, we define a novel methodology that retains only radial branches that can be implemented with one-dimensional finite impulse response filters. This model is subsequently simplified by selecting a subset of directions using an ad hoc procedure. Both models are evaluated in terms of accuracy in the time and frequency domains and complexity, and are compared with other models described in the literature. The evaluation is conducted using a low-voltage silicon RF driver amplifier and a 5-W PA, which are characterized at different levels with diverse modulation formats, including wideband code-division multiple-access (WCDMA) and orthogonal frequency-division multiplexed (OFDM) signals. In all cases, comparison of the measured and simulated responses confirms the effectiveness of the proposed approach.

Neural Systems as Nonlinear Filters

Abstract: Experimental data show that biological synapses behave quite differently from the symbolic synapses in all common artificial neural network models. Biological synapses are dynamic; their “weight” changes on a short timescale by several hundred percent in dependence of the past input to the synapse. In this article we address the question how this inherent synaptic dynamics (which should not be confused with long term learning) affects the computational power of a neural network. In particular, we analyze computations on temporal and spatiotemporal patterns, and we give a complete mathematical characterization of all filters that can be approximated by feedforward neural networks with dynamic synapses. It turns out that even with just a single hidden layer, such networks can approximate a very rich class of nonlinear filters: all filters that can be characterized by Volterra series. This result is robust with regard to various changes in the model for synaptic dynamics. Our characterization result provides for all nonlinear filters that are approximable by Volterra series a new complexity hierarchy related to the cost of implementing such filters in neural systems.

An adaptive nonlinear prefilter for compensation of distortion in nonlinear systems

Abstract: This article concerns the linearization of a nonlinear system by connecting a nonlinear Volterra prefilter tandemly with the nonlinear system and by adaptively adjusting the coefficients of the prefilter. "A nonlinear filtered-x LMS algorithm" for updating the coefficients of a nonlinear prefilter, as proposed, is shown to be viewed as an extension of the well-known filtered-x LMS algorithm.