Related papers: Control of Volterra systems with scalar kernels

The Volterra integral equations of the first kind with piecewise smooth kernel are considered. Such equations appear in the theory of optimal control of the evolving systems. The existence theorems are proved. The method for constructing…

This paper provides a Feller's test for explosions of one-dimensional continuous stochastic Volterra processes of convolution type. The study focuses on dynamics governed by nonsingular kernels, which preserve the semimartingale property of…

This work aims to bridge the gap between pure and applied research on scalar, linear Volterra equations by examining five major classes: integral and integro-differential equations with completely monotone kernels, such as linear…

We study linear-quadratic optimal control problems for Voterra systems, and problems that are linear-quadratic in the control but generally nonlinear in the state. In the case of linear-quadratic Volterra control, we obtain sharp necessary…

As previously shown, the direct extension of the impulse invariance principle to Volterra kernels has to be modified in order to provide a condition for the exact modeling of mixed-signal chains. At first sight this would seem to seriously…

In the paper some sufficient condition for the nonlinear integral operator of the Volterra type to be a diffeomorphism defined on the space of absolutely continuous functions are formulated. The proof relies on consideration of the…

Volterra analysis and its variants have long been prominent among methods for modeling multi-input non-linear systems. The product of Volterra analysis, the Volterra kernels, are particularly suited to quantifying intra- and inter-input…

We introduce new fractional operators of variable order on isolated time scales with Mittag-Leffler kernels. This allows a general formulation of a class of fractional variational problems involving variable-order difference operators. Main…

The existence of weak solutions is established for stochastic Volterra equations with time-inhomogeneous coefficients allowing for general kernels in the drift and convolutional or bounded kernels in the diffusion term. The presented…

The systems of nonlinear Volterra integral equations of the first kind with jump discontinuous kernels are studied. The iterative numerical method for such nonlinear systems is proposed. Proposed method employs the modified…

We study some mapping properties of Volterra type integral operators and composition operators on model spaces. We also discuss and give out a couple of interesting open problems in model spaces where any possible solution of the problems…

In this paper, sufficient conditions are established for the existence results of fractional order semilinear Volterra integrodifferential equations in Banach spaces. The results are obtained by using the theory of fractional cosine…

We propose a new theoretical framework that exploits convolution kernels to transform a Volterra-type path-dependent (non-Markovian) stochastic process into a standard (Markovian) diffusion process. Remarkably, it is also possible to go…

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…

This study aims to discuss the existence and uniqueness of solution of fuzzy Volterra integral equation with piecewise continuous kernel. Such problems appears in many balance problems for hereditary dynamic systems, e.g. in electric load…

We are concerned with nonparametric hypothesis testing of time series functionals. It is known that the popular autoregressive sieve bootstrap is, in general, not valid for statistics whose (asymptotic) distribution depends on moments of…

This article studies Volterra evolution equations from the point of view of control theory, in the case that the generator of the underlying semigroup has a Riesz basis of eigenvectors. Conditions for admissibility of the system's control…

The sufficient conditions for existence and uniqueness of continuous solutions of the Volterra operator equations of the first kind with piecewise continuous kernel are derived. The asymptotic approximation of the parametric family of…

This paper focuses on the systems theory of bilinear dynamical systems using the Volterra series representation. The main contributions are threefold. First, we gain an input-output representation in the frequency domain, where the Laplace…

This paper deals with fractional-order controlled systems and fractional-order controllers in the frequency domain. The mathematical description by fractional transfer functions and properties of these systems are presented. The new ways…