A Reduced Order Controller for Output Tracking of a Kelvin-Voigt Beam

Asymptotic behavior of the transmission Euler-Bernoulli plate and wave equation with a localized Kelvin-Voigt damping

Let a fourth and a second order evolution equations be coupled via the interface by transmission conditions, and suppose that the first one is stabilized by a localized distributed feedback. What will then be the effect of such a partial stabilization on the decay of solutions at infinity? Is the behavior of the first component sufficient to stabilize the second one? The answer given in this paper is that sufficiently smooth solutions decay logarithmically at infinity even the feedback dissipation affects an arbitrarily small open subset of the interior. The method used, in this case, is based…

具有局部退化凯尔文-沃伊格阻尼的弦的稳定性分析

Sharp Stability of a String with Local Degenerate Kelvin-Voigt Damping

本文研究了具有局部退化凯尔文-沃伊格阻尼的弹性弦方程的渐进行为，针对不同α值，推导出更优的多项式衰减率，并与最优衰减率一致。

Inverse Problems of Identifying the Unknown Transverse Shear Force in the Euler-Bernoulli Beam with Kelvin-Voigt Damping

In this paper, we study the inverse problems of determining the unknown transverse shear force $g(t)$ in a system governed by the damped Euler-Bernoulli equation $ρ(x)u_{tt}+μ(x)u_t+ (r(x)u_{xx})_{xx}+ (κ(x)u_{xxt})_{xx}=0, ~(x,t)\in (0,\ell)\times(0,T],$ subject to the boundary conditions $u(0,t) =0$, $u_{x}(0,t)=0$, $\left[r(x)u_{xx}+κ(x)u_{xxt}\right]_{x=\ell} =0$, $-\left[\big(r(x)u_{xx}+κ(x)u_{xxt}\big)_{x}\right]_{x=\ell}=g(t)$, $t\in [0,T]$, from the measured deflection $ν(t):=u(\ell,t)$, $t \in [0,T]$, and from the bending moment $ω(t):=-\left( r(0)u_{xx}(0,t)+κ(0)u_{xxt}(0,t) \right)$…

波系统中Kelvin-Voigt阻尼的边界到位移渐近增益

Boundary-to-Displacement Asymptotic Gains for Wave Systems With Kelvin-Voigt Damping

本文研究了具有Kelvin-Voigt阻尼和粘性阻尼的弦振动系统在边界扰动下的渐近增益，通过L2范数和空间sup范数分析，证明了在L2范数下无需假设阻尼系数即可获得渐近增益，并采用特征函数展开和小增益论证方法推导上界，频率分析方法推导下界。

Energy decay estimates of elastic transmission wave/beam systems with a local Kelvin-Voigt damping

We consider a beam and a wave equations coupled on an elastic beam through transmission conditions. The damping which is locally distributed acts through one of the two equations only; its effect is transmitted to the other equation through the coupling. First we consider the case where the dissipation acts through the beam equation. Using a recent result of Borichev and Tomilov on polynomial decay characterization of bounded semigroups we provide a precise decay estimates showing that the energy of this coupled system decays polynomially as the time variable goes to infinity. Second, we discu…

Reduced Order Controller Design for Robust Output Regulation

We study robust output regulation for parabolic partial differential equations and other infinite-dimensional linear systems with analytic semigroups. As our main results we show that robust output tracking and disturbance rejection for our class of systems can be achieved using a finite-dimensional controller and present algorithms for construction of two different internal model based robust controllers. The controller parameters are chosen based on a Galerkin approximation of the original PDE system and employ balanced truncation to reduce the orders of the controllers. In the second part o…

Finite-Dimensional Controllers for Robust Regulation of Boundary Control Systems

We study the robust output regulation of linear boundary control systems by constructing extended systems. The extended systems are established based on solving static differential equations under two new conditions. We first consider the abstract setting and present finite-dimensional reduced order controllers. The controller design is then used for particular PDE models: high-dimensional parabolic equations and beam equations with Kelvin-Voigt damping. Numerical examples will be presented using Finite Element Method.