Stabilization by switching control methods
Kaïs Ammari, Serge Nicaise, Cristina Pignotti
本文考虑一类带开关的波动方程的镇定问题。我们证明指数稳定性结果适当的阻尼系数。主要结果的证明是基于D'Alembert公式和一些能量估计。
In this paper we consider some stabilization problems for the wave equation with switching. We prove exponential stability results for appropriate damping coefficients. The proof of the main results is based on D'Alembert formula and some energy estimates.
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Numerical stabilization method by switching time-delay
该研究基于切换时滞稳定化理论，提出一种演化系统的新型数值稳定策略，并在一维情形下用数值近似技术实现，实验验证了理论结果。
This paper deals with the boundary stabilization problem of a one-dimensional wave equation with a switching time-delay in the boundary. We show that the problem is well-posed in the sense of semigroups theory of linear operators. Then, we provide a theoretical and numerical study of the exponential stability of the system under an appropriate delay coefficient.
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Stability results for second-order evolution equations with memory and switching time-delay
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Rapid stabilization and finite time stabilization of the bilinear Schrödinger equation
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Global controllability and stabilization for the nonlinear Schrödinger equation on some compact manifolds of dimension 3
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我们提出的例子，指数稳定的阻尼波方程的紧流形上的几何控制条件不满足的情况下。这是从一个动力学参数，涉及一个拓扑压力的一个适当的不受控制的设置。
We prove that the thickness property is a necessary and sufficient geometric condition that ensures the (rapid) stabilization or the approximate null-controllability with uniform cost of a large class of evolution equations posed on the whole space $\mathbb R^n$. These equations are associated with operators of the form $F(\vert D_x\vert)$, the function $F:[0,+\infty)\rightarrow\mathbb R$ being continuous and bounded from below. We also provide explicit feedbacks and constants associated with these stabilization properties. The notion of thickness is known to be a necessary and sufficient cond…
Global controllability and stabilization of the wave maps equation from a circle to a sphere
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Global stabilization and emergence tracking via aquatic control in an age-structured mosquito model
针对疟疾媒介蚊子种群动态，本文构建年龄结构非自治logistic模型，提出结合反馈与前馈的水生阶段控制策略，实现羽化种群的全局渐近稳定及时变轨迹追踪，结果经数值模拟验证。
In this article, global stabilization results for the two dimensional (2D) viscous Burgers' equation, that is, convergence of unsteady solution to its constant steady state solution with any initial data, are established using a nonlinear Neumann boundary feedback control law. Then, applying $C^0$-conforming finite element method in spatial direction, optimal error estimates in $L^\infty(L^2)$ and in $L^\infty(H^1)$- norms for the state variable and convergence result for the boundary feedback control law are derived. All the results preserve exponential stabilization property. Finally, severa…
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