Abstract

A spatially discrete control law is proposed for a class of systems described by scalar linear differential equations of parabolic and hyperbolic types with unknown parameters and disturbances. A finite set of discrete measurements (with respect to the spatial variable) of the plant state is available. The control law depends on a function that depends on the spatial variable and on a finite set of measurements of the plant state. Examples of this function, which allows realizing the control signal only at certain intervals in the spatial variable and providing lower control costs than some other analogs, are given. The exponential stability of the closed-loop system and robustness with respect to interval uncertain parameters of the plant and exogenous bounded disturbances are proved. Numerical modeling examples confirm the results of calculations and show the efficiency of the algorithm compared with some existing analogs.

中文翻译：

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抛物线型和双曲线型标量线性分布植物的空间离散控制

摘要

针对由未知参数和扰动的抛物线和双曲线型的标量线性微分方程描述的一类系统，提出了一种空间离散的控制律。可获得一组有限的离散状态（相对于空间变量）的植物状态。控制定律取决于一个功能，该功能取决于空间变量和一组有限的植物状态测量值。给出了此功能的示例，该功能允许仅在空间变量中的特定间隔处实现控制信号，并提供比某些其他类似物更低的控制成本。证明了闭环系统的指数稳定性和针对植物的区间不确定性参数以及外生有界扰动的鲁棒性。