Related papers: Control of Volterra systems with scalar kernels

Solving systems of non-autonomous ordinary differential equations (ODE) is a crucial and often challenging problem. Recently a new approach was introduced based on a generalization of the Volterra composition. In this work, we explain the…

This paper studies existence and uniqueness of solutions to generalized Volterra integral equations. Since our proof for existence and uniqueness does not make use of Banach fixed point theorem unlike the previous papers focused on this…

The main purpose of this paper is to apply the theory of vector lattices and the related abstract modular convergence to the context of Mellin-type kernels and (non)linear vector lattice-valued operators, following the construction of an…

This paper focuses on the optimal control of a class of stochastic Volterra integral equations. Here the coefficients are regular and not assumed to be of convolution type. We show that, under mild regularity assumptions, these equations…

We present a family of kernels for analysis of data generated by dynamical systems. These so-called cone kernels feature an explicit dependence on the dynamical vector field operating in the phase-space manifold, estimated empirically…

This paper deals with fractional-order controlled systems and fractional-order controllers in the discrete domain. The mathematical description by the fractional difference equations and properties of these systems are presented. A…

The present paper plans to examine the existence, uniqueness and data dependence of the solution of the fractional functional differential equation with the abstract operator of Volterra, in the context of the Picard operators. We present…

Perturbing a system far away from equilibrium via a time dependent protocol can formally be described by a nonlinear Volterra series expansion. Here we derive identities for the nonlinear memory kernels arising in such nonlinear expansion,…

A new technique based on superposition of two speckle patterns is proposed and demonstrated for controlled modulation of the spatial polarization distribution of the resultant speckle. It is demonstrated both theoretically and…

Volterra series are especially useful for nonlinear system identification, also thanks to their capability to approximate a broad range of input-output maps. However, their identification from a finite set of data is hard, due to the curse…

Data sites selected from modeling high-dimensional problems often appear scattered in non-paternalistic ways. Except for sporadic clustering at some spots, they become relatively far apart as the dimension of the ambient space grows. These…

Implementing a component-based system in a distributed way so that it ensures some global constraints is a challenging problem. We consider here abstract specifications consisting of a composition of components and a controller given in the…

We obtain necessary conditions of optimality for impulsive Volterra integral equations with switching and impulsive controls, with variable impulse time-instants. The present work continues and complements our previous work on impulsive…

The aim of the paper is to study an optimal control problem on infinite horizon for an infinite dimensional integro-differential equation with completely monotone kernelskernels, where we assume that the noise enters the system when we…

We study the class of continuous polynomial Volterra processes, which we define as solutions to stochastic Volterra equations driven by a continuous semimartingale with affine drift and quadratic diffusion matrix in the state of the…

Based on the notion of paracontrolled distributions, we provide existence and uniqueness results for rough Volterra equations of convolution type with potentially singular kernels and driven by the newly introduced class of convolutional…

The aim of this work is to present, in self-contained form, results concerning fundamental and the most important questions related to linear stochastic Volterra equations of convolution type. The paper is devoted to study the existence and…

This work builds on the Volterra series formalism presented in [D. W. Dreisigmeyer and P. M. Young, J. Phys. A \textbf{36}, 8297, (2003)] to model nonconservative systems. Here we treat Lagrangians and actions as `time dependent' Volterra…

In this paper, the inverse spectral problem is applied to the integration of a periodic Volterra chain. A generalization of the Lagrange interpolation formula has been made.

We consider a terminal control problem for processes governed by a nonlinear system of fractional ODEs. In order to show existence of the control, we first consider the linear counterpart of the system and reprove a number of classical…