This paper is concerned with the problem of boundary observer-based finite-time output feedback control for a heat system with Neumann boundary condition and Dirichlet boundary actuator. In this system, it is endowed a single sensor at the left boundary and actuator at the right boundary. First, a backstepping finite-time observer is designed. Based on linear switching observer gains with state-dependent switching, the proposed observer estimates the system state variables in a finite-time only using one displacement boundary measurement. Then, an observer-based linear switching output feedback control with state-dependent switching is presented, which steers any solution of the output feedback closed-loop system to zero in a finite-time. Finally, the simulation results are provided to support the theoretical results.

本文涉及具有诺伊曼边界条件和Dirichlet边界执行器的热系统基于边界观测器的有限时间输出反馈控制问题。在该系统中，在左边界处赋予单个传感器，在右边界处赋予致动器。首先，设计了一个后退的有限时间观测器。基于具有状态相关切换的线性切换观测器增益，提出的观测器仅使用一个位移边界测量值即可在有限时间内估算系统状态变量。然后，提出了具有状态相关切换的基于观察者的线性切换输出反馈控制，该控制将输出反馈闭环系统的任何解决方案在有限时间内转向零。最后，提供了仿真结果以支持理论结果。