Related papers: Numerical approximation of the boundary control fo…
This work proposes a method for solving linear stochastic optimal control (SOC) problems using sum of squares and semidefinite programming. Previous work had used polynomial optimization to approximate the value function, requiring a high…
Novel fully discrete schemes are developed to numerically approximate a semilinear stochastic wave equation driven by additive space-time white noise. Spectral Galerkin method is proposed for the spatial discretization, and exponential time…
In this paper, we deal with the boundary controllability and boundary stabilizability of the 1D wave equation in non-cylindrical domain of the form ($\alpha (t)<x<\beta (t)$). By using the characteristics method, we prove under a natural…
We present a spectral approach to design approximation algorithms for network design problems. We observe that the underlying mathematical questions are the spectral rounding problems, which were studied in spectral sparsification and in…
The paper is devoted to the exact controllability of a system of coupled abstract wave equations when the control is exerted on a part of the boundary by means of one control. We give a Kalman type condition and give a description of the…
We propose a compressive spectral collocation method for the numerical approximation of Partial Differential Equations (PDEs). The approach is based on a spectral Sturm-Liouville approximation of the solution and on the collocation of the…
- We discuss the approximation of distributed null controls for partial differential equations. The main purpose is to determine an approximation of controls that drives the solution from a prescribed initial state at the initial time to…
We consider applications of the Boundary Control (BC) method to generalized spectral estimation problems and to inverse source problems. We derive the equations of the BC method for this problems and show that solvability of this equations…
Numerical relativity has traditionally been pursued via finite differencing. Here we explore pseudospectral collocation (PSC) as an alternative to finite differencing, focusing particularly on the solution of the Hamiltonian constraint (an…
To achieve control objectives for extremely large-scale complex networks using standard methods is essentially intractable. In this work a theory of the approximate control of complex network systems is proposed and developed by the use of…
We present a novel spectral method for the Allen-Cahn equation on spheres, eliminating the reliance on conventional quadrature exactness conditions. By replacing these conditions with a restricted isometry relation derived from…
We present and analyze a new method for solving optimal control problems for Volterra integral equations, based on approximating the controlled Volterra integral equations by a sequence of systems of controlled ordinary differential…
In this chapter, we present some recent progresses on the numerics for stochastic distributed parameter control systems, based on the \emph{finite transposition method} introduced in our previous works. We first explain how to reduce the…
We study the exact controllability for spatially periodic water waves with surface tension, by localized exterior pressures applied to free surfaces. We prove that in any dimension, the exact controllability holds within arbitrarily short…
In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…
Neural field equations offer a continuous description of the dynamics of large populations of synaptically coupled neurons. This makes them a convenient tool to describe various neural processes, such as working memory, motion perception,…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
In this paper we present a spectral collocation method for the fast evaluation of the Landau collision operator for plasma physics, which allows us to obtain spectrally accurate numerical solutions. The method is inspired by the seminal…
We propose an approximation of nonlinear renewal equations by means of ordinary differential equations. We consider the integrated state, which is absolutely continuous and satisfies a delay differential equation. By applying the…
Pseudospectral time domain (PSTD) methods are widely used in many branches of acoustics for the numerical solution of the wave equation, including biomedical ultrasound and seismology. The use of the Fourier collocation spectral method in…