SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 220-242, February 2024.
Abstract. Stabilization of a class of time-varying parabolic equations with uncertain input data using receding horizon control (RHC) is investigated. The diffusion coefficient and the initial function are prescribed as random fields. We consider both cases: uniform and log-normal distributions of the diffusion coefficient. The controls are chosen to be finite-dimensional and enter into the system as a linear combination of finitely many indicator functions (actuators) supported in open subsets of the spatial domain. Under suitable regularity assumptions, we study the expected (averaged) stabilizability of the RHC-controlled system with respect to the number of actuators. An upper bound is also obtained for the failure probability of RHC in relation to the choice of the number of actuators and parameters in the equation.

中文翻译：

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不确定性下非自治抛物型方程的RHC稳定性分析

SIAM 控制与优化杂志，第 62 卷，第 1 期，第 220-242 页，2024 年 2 月。
摘要。研究了使用后退地平线控制 (RHC) 来稳定一类具有不确定输入数据的时变抛物线方程。扩散系数和初始函数被规定为随机场。我们考虑两种情况：扩散系数的均匀分布和对数正态分布。选择的控件是有限维的，并作为空间域开放子集中支持的有限多个指示函数（执行器）的线性组合进入系统。在适当的规律性假设下，我们研究 RHC 控制系统相对于执行器数量的预期（平均）稳定性。还获得了与方程中执行器数量和参数选择相关的 RHC 失效概率的上限。