相关论文: Controlling roughening processes in the stochastic…
The problem of controlling and stabilising solutions to the Kuramoto-Sivashinsky equation is studied in this paper. We consider a generalised form of the equation in which the effects of an electric field and dispersion are included. Both…
In this paper, two boundary controllers are proposed to stabilize the origin of the nonlinear Kuramoto-Sivashinsky equation under intermittent measurements. More precisely, the spatial domain is divided into two sub-domains. The state of…
In this work, we address the existence of insensitizing controls for a nonlinear coupled system of fourth- and second-order parabolic equations known as the stabilized Kuramoto-Sivashinsky model. The main idea is to look for controls such…
We consider the application of feedback control strategies with point actuators to stabilise desired interface shapes. We take a multidimensional Kuramoto--Sivashinsky equation as a test case; this equation arises in the study of thin…
This paper is concerned with the local output feedback stabilization of a nonlinear Kuramoto-Sivashinsky equation. The control is located at the boundary of the domain while the measurement is selected as a Neumann trace. This choice of…
We consider a space-time finite element method on fully unstructured simplicial meshes for optimal sparse control of semilinear parabolic equations. The objective is a combination of a standard quadratic tracking-type functional including a…
This paper is concerned with optimal control problems for parabolic partial differential equations with pointwise in time switching constraints on the control. A standard approach to treat constraints in nonlinear optimization is…
This paper presents a method to approximately solve stochastic optimal control problems in which the cost function and the system dynamics are polynomial. For stochastic systems with polynomial dynamics, the moments of the state can be…
This paper deals with the null controllability of a coupled parabolic system, which is Kuramoto-Sivashinsky-Korteweg-de Vries equation coupled with heat equation through first order derivative. More precisely, we prove the null…
In this article the robust Stackelberg controllability (RSC) problem is studied for a nonlinear fourth-order parabolic equation, namely, the Kuramoto-Sivashinsky equation. When three external sources are acting into the system, the RSC…
We investigate the robust Stackelberg null controllability of a one-dimensional forward linear stochastic Kuramoto--Sivashinsky--Korteweg--de Vries (KS--KdV) equation. The control framework is formulated as a hierarchical Stackelberg game…
This paper deals with a stochastic optimal feedback control problem for the controlled stochastic partial differential equations. More precisely, we establish the existence of stochastic optimal feedback control for the controlled…
In this paper, we investigate an optimal control problem governed by parabolic equations with measure-valued controls over time. We establish the well-posedness of the optimal control problem and derive the first-order optimality condition…
- 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 analyse the nonlinear Kuramoto--Sivashinsky equation to develop accurate discretisations modeling its dynamics on coarse grids. The analysis is based upon centre manifold theory so we are assured that the discretisation accurately models…
This paper addresses sampled-data control of 2D Kuramoto-Sivashinsky equation over a rectangular domain. We suggest to divide the 2D rectangular into N sub-domains, where sensors provide spatially averaged or point state measurements to be…
It is shown that an oblique projection based feedback control is able to stabilize the state of the Kuramoto-Sivashinsky equation, evolving in rectangular domains, to a given time-dependent trajectory. The number of actuators is finite and…
The present study investigates a linear-quadratic Dirichlet control problem governed by a non-coercive elliptic equation posed on a possibly non-convex polygonal domain. Tikhonov regularization is carried out in an energy seminorm. The…
This paper presents a novel method to synthesize stochastic control Lyapunov functions for a class of nonlinear, stochastic control systems. In this work, the classical nonlinear Hamilton-Jacobi-Bellman partial differential equation is…
In this paper, we continue the study of some controllability issues for the forward stochastic parabolic equation with dynamic boundary conditions. The main novelty in the present paper consists of considering only one control without extra…