Feedback control for random, linear hyperbolic balance laws

A boundary feedback analysis for input-to-state-stabilisation of non-uniform linear hyperbolic systems of balance laws with additive disturbances

A boundary feedback stabilisation problem of non-uniform linear hyperbolic systems of balance laws with additive disturbance is discussed. A continuous and a corresponding discrete Lyapunov function is defined. Using an input-to-state-stability (ISS) $ L^2- $Lyapunov function, the decay of solutions of linear systems of balance laws is proved. In the discrete framework, a first-order finite volume scheme is employed. In such cases, the decay rates can be explicitly derived. The main objective is to prove the Lyapunov stability for the $L^2$-norm for linear hyperbolic systems of balance laws wi…

一种确定一维线性双曲平衡律最小零控时间的方法

A method to determine the minimal null control time of 1D linear hyperbolic balance laws

该研究提出一种方法，可在系数足够正则的条件下，通过单侧边界控制确定一维一阶线性双曲系统零能控性的最小控制时间。

Finite-time boundary stabilization of general linear hyperbolic balance laws via Fredholm backstepping transformation $\star$

This paper is devoted to a simple and new proof on the optimal finite control time for general linear coupled hyperbolic system by using boundary feedback on one side. The feedback control law is designed by first using a Volterra transformation of the second kind and then using an invertible Fredholm transformation. Both existence and invertibility of the transformations are easily obtained.

An analysis of the input-to-state-stabilisation of linear hyperbolic systems of balance laws with boundary disturbances

In this paper, a linear hyperbolic system of balance laws with boundary disturbances in one dimension is considered. An explicit candidate Input-to-State Stability (ISS)-Lyapunov function in $ L^2- $norm is considered and discretised to investigate conditions for ISS of the discrete system as well. Finally, experimental results on test examples including the Saint-Venant equations with boundary disturbances are presented. The numerical results demonstrate the expected theoretical decay of the Lyapunov function.

一维线性双曲平衡律内部控制精确能控的最小控制时间

The minimal control time for the exact controllability by internal controls of 1D linear hyperbolic balance laws

该研究针对控制量与状态变量数量相等的一维线性双曲平衡律，探究其内部控制能控性，完整刻画了空间支撑为任意开子集时精确能控的最小控制时间。

通过积分差分控制实现一维线性双曲型平衡律的镇定及其在网络镇定中的应用

Stabilization of 1D Linear Hyperbolic Balance Laws by Integral Difference Control and Application to Networks Stabilization

研究一阶线性双曲型平衡律在一般驱动下的指数镇定，提出统一方法，整合多种欠驱动配置，应用于含环网络，基于反步变换和积分差分方程设计控制律，增益由降秩程序和插值方程解构建，通过数值模拟验证对特定循环网络的有效性。