学习一个半全局镇定半线性抛物型方程的最优反馈算子

Exponential stabilization of the semilinear heat equation with nonlocal boundary conditions

The present work is devoted to the problem of boundary stabilization of the semilinear 1-D heat equation with nonlocal boundary conditions. The stabilizing controller is finite-dimensional, linear, given in an explicit form, involving only the eigenfunctions of the Laplace operator with nonlocal boundary conditions.

Stabilization of semilinear PDE's, and uniform decay under discretization

These notes are issued from a short course given by the author in a summer school in Chamb{é}ry in June 2015. We consider general semilinear PDE's and we address the following two questions: 1) How to design an efficient feedback control locally stabilizing the equation asymptotically to 0? 2) How to construct such a stabilizing feedback from approximation schemes? To address these issues, we distinguish between parabolic and hyperbolic semilinear PDE's. By parabolic, we mean that the linear operator underlying the system generates an analytic semi-group. By hyperbolic, we mean that this opera…

Boundary sampled-data feedback stabilization for parabolic equations

The aim of this work is to design an explicit finite dimensional boundary feedback controller of sampled-data form for locally exponentially stabilizing the equilibrium solutions to semilinear parabolic equations. The feedback controller is expressed in terms of the eigenfunctions corresponding to unstable eigenvalues of the linearized equation. This stabilizing procedure is applicable for any sampling rate, not necessary to be small enough, and it tends to the continuous-times version when the sampling period tends to zero.

Semiglobal exponential stabilization of nonautonomous semilinear parabolic-like systems

It is shown that an explicit oblique projection nonlinear feedback controller is able to stabilize semilinear parabolic equations, with time-dependent dynamics and with a polynomial nonlinearity. The actuators are typically modeled by a finite number of indicator functions of small subdomains. No constraint is imposed on the sign of the polynomial nonlinearity. The norm of the initial condition can be arbitrarily large, and the total volume covered by the actuators can be arbitrarily small. The number of actuators depend on the operator norm of the oblique projection, on the polynomial degree …

基于POD的模型预测控制在半线性抛物型PDE中的渐近稳定性

Asymptotic Stability of POD based Model Predictive Control for a semilinear parabolic PDE

本文利用非线性模型预测控制方法，结合POD降阶策略，对半线性抛物型PDE进行稳定反馈控制设计，并通过数值实验验证了算法的渐近稳定性。

多项式逼近高维Hamilton-Jacobi-Bellman方程及其在反馈控制半线性抛物型PDEs中的应用

Polynomial approximation of high-dimensional Hamilton-Jacobi-Bellman equations and applications to feedback control of semilinear parabolic PDEs

本文提出了一种数值逼近高维Hamilton-Jacobi-Bellman方程的程序，用于最优反馈控制问题，该方法结合了伪谱格点逼近PDE动力学和迭代方法求解非线性HJB方程，主要贡献是通过分离多项式逼近方法求解线性广义HJB方程，从而获得稳定反馈控制。