SIAM Journal on Control and Optimization, Volume 59, Issue 1, Page 464-488, January 2021.
A Luenberger type dynamical observer is proposed for estimation of the full state of a nonautonomous linear parabolic equation, from a finite-dimensional output. The output is given by average-like measurements of the state on small regions. The state estimate given by the observer converges exponentially to the real state, as time increases. The operator which injects the output into the dynamics of the observer is explicit and involves an appropriate oblique projection. Results of numerical simulations are presented showing the exponential stability of the error dynamics, and thus showing the estimating performance of the observer.

中文翻译：

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非自治线性抛物线型方程的斜投影指数动力学观测器

SIAM控制与优化杂志，第59卷，第1期，第464-488页，2021年1月。
提出了一种Luenberger型动态观测器，用于从有限维输出估算非自治线性抛物方程的完整状态。通过在小区域上对状态进行类似平均的测量来提供输出。随着时间的增加，观察者给出的状态估计将指数收敛到真实状态。将输出注入观察者动态的操作员是明确的，并且涉及适当的倾斜投影。数值模拟的结果显示了误差动态的指数稳定性，从而显示了观察者的估计性能。