非自治半线性抛物型方程的半全局斜投影指数动态观测器
Semiglobal oblique projection exponential dynamical observers for nonautonomous semilinear parabolic-like equations
AI总结：
本文提出一种Luenberger型动态观测器，通过有限次小区域平均测量输出，实现非自治半线性抛物型方程全状态的半全局指数收敛估计，并利用显式斜投影输出注入算子保证误差动力学稳定。
摘要：
通过Luenberger型动态观测器实现了非自治半线性抛物型方程全状态的估计。该估计基于由状态在多个小区域上的有限次平均测量所给出的输出。随着时间增加，观测器给出的状态估计指数收敛至真实状态。结果是半全局的，即只要取足够多（取决于初始条件范数）的测量次数，误差动力学即可对任意给定的初始条件保持稳定。输出注入算子是显式的，并涉及一个合适的斜投影。数值模拟的结果展示了误差动力学的指数稳定性。
英文摘要：
The estimation of the full state of a nonautonomous semilinear parabolic equation is achieved by a Luenberger type dynamical observer. The estimation is derived from an output given by a finite number of average measurements of the state on small regions. The state estimate given by the observer converges exponentially to the real state, as time increases. The result is semiglobal in the sense that the error dynamics can be made stable for an arbitrary given initial condition, provided a large enough number of measurements, depending on the norm of the initial condition, is taken. The output injection operator is explicit and involves a suitable oblique projection. The results of numerical simulations are presented showing the exponential stability of the error dynamics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
