Showing papers on "Volterra series published in 1977"

The existence and uniqueness of Volterra series for nonlinear systems

Abstract: Given an input-output map described by a nonlinear control system \dot{x}=f(x,u) and nonlinear output y=h(x) , we present a simple straightforward means for obtaining a series representation of the output y(t) in terms of the input u(t) . When the control enters linearly, \dot{x} =f(x)+ ug(x) , the method yields the existence of a Volterra series representation. The proof is constructive and explicitly exhibits the kernels. It depends on standard mathematical tools such as the Fundamental Theorem of Calculus and the Cauchy estimates for the Taylor series coefficients of analytic functions. In addition, the uniqueness of Volterra series representations is discussed.

Functional expansions for the response of nonlinear differential systems

Abstract: This paper is concerned with representing the response of nonlinear differential systems by functional expansions. An abstract theory of variational expansions, similar to that of L. M. Graves (1927), is developed. It leads directly to concrete expressions (multilinear integral operators) for the functionals of the expansions and sets conditions on the differential systems which insure that the expansions give reasonable approximations of the response. Similarly, it is shown that the theory of analytic functions in Banach spaces leads directly to conditions which imply uniform convergence of functional series. The main results on differential systems are summarized in a set of theorems, some of which overlap and extend the recent results of Brockett on Volterra series representations for the response of linear analytic differential systems. Other theorems apply to more general nonlinear differential systems. They provide a rigorous foundation for a large body of previous research on Volterra series expansions. The multilinear integral operators are obtained from systems of differential equations which characterize exactly the variations. These equations are of much lower order than those obtained by the technique of Carleman. A nonlinear feedback system serves as an example of an application of the theory.

Bibliography on Volterra series hermite functional expansions and related subjects

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Intermodulation Distortion Analysis of Reflection-Type IMPATT Amplifiers Using Volterra Series Representation

Abstract: Intermodulation distortion generated in a stable IMPATT amplifier is analyzed using Volterra series representation. An IMPATT amplifier model, which takes into account the interaction between the nonlinearities of the diode and its embedding circuitry, is described. The Volterra transfer functions are derived for this model. Nonlinear terms up to and including the fifth order are considered. Intermodulation distortion products are calculated for a low-level input signal consisting of two tones. The results of this analysis are extrapolated into the direction of increasing output power in order to obtain the third-order intercept point. Further, closed form expressions for the third-order intermodulation IM/sub 3/ and intercept point P/sub I/ are derived. The distortion of a specific 6-GHz IMPATT amplifier is evaluated for illustrative purposes; the predicted distortion behavior compares favorably with experimental results.

On the internal realization of nonlinear behaviors

Abstract: Publisher Summary This chapter focuses on the internal realization of nonlinear behaviors. The algebraic realization theory of linear input/output (i/o) maps is well developed and understood. Linear methods are still useful when treating certain special types of i/o-maps, namely, bilinear i/o-maps and internally-bilinear i/o-maps. This chapter presents an approach designed to deal with a new class of nonlinear (shift-invariant, causal) discrete-time i/o-maps, polynomial maps. This class is large enough to include a wide range of practical examples while at the same time restricted enough to permit the application of useful algebraic tools. An i/o map operates on sequences of input values to produce corresponding sequences of output values. The output values calculated by a polynomial i/o-map f are the sums of products of previous input values. A polynomial i/o-map f is specified through a formal power series called the (discrete) Volterra series of f.

Sensitivity Study of Control Parameters during Underway Replenishment Simulations Including Approximate Nonlinear Sea Effects.

Abstract: : This report describes the fourth phase of the development of a hybrid computer simulation of two ships during underway replenishment (UNREP) operations. Emphasis was placed on performing sensitivity analysis of the maneuvering control parameters. Some approximate nonlinear sea state excitations acting on the ships' hulls due to a specific irregular sea were added to the simulation model. The mathematical model for both the nonlinear force and moment excitations was developed by using the Volterra Series mathematical formalism. The forces and moments were represented during the simulation by time series. The sea state was defined in the UNREP simulation by the Pierson-Moskowitz Spectra. The simulation incorporating some approximate nonlinear sea state excitations, together with an automatic controller on each ship, was used for control variable sensitivity studies.

A contribution to the theory of non-linear distributed-parameter systems

Abstract: A now application of Volterra series has been made to characterize the input-output behaviour of a class of non-linear distributed parameter systems This application leads to the transformation of a non-linear distributed-parameter system into an infinite set of non-linear lumped parameter systems The results have been illustrated by two examples

Functional analysis and identification of separable nonlinear control systems using pseudorandom inputs.

Abstract: The analysis and identification of separable nonlinear single valued systems is carried out from a functional standpoint, by modifying the Volterra series to separate bias and steady state gain from dynamic effects. This analysis is applied to the development of generalised expressions for output bias, variance and correlation functions of nonlinear systems with Gaussian or pseudo-random inputs. An identification procedure is then developed and applied to the testing of both simulated systems, and an electrohydraulic servomotor. An error analysis is carried out showing the limitations of the method, and procedures derived designed at eliminating the effects of random and cyclic noise.