标题： 具有无限维外系统的正则线性系统的鲁棒控制器 显示英文标题

标题： Robust Controllers for Regular Linear Systems with Infinite-Dimensional Exosystems

摘要： 我们为具有非光滑参考信号和扰动信号的正则线性系统构建了两种误差反馈控制器，用于鲁棒输出跟踪和干扰抑制。 我们证明，对于足够光滑的信号，输出将以依赖于该系统传递函数在虚轴上行为的速度收敛到参考信号。 此外，我们构造了一个可以针对系统中某一类不确定性设计以实现鲁棒性的控制器，并提出了一种新的控制器结构，用于输出跟踪和干扰抑制而无需鲁棒性要求。 我们还推广了具有边界干扰的正则线性系统以及具有无界输入和输出算子的控制器的内部模型原理。 通过一个例子说明了控制器的构造过程，在该例子中，我们考虑二维热方程在边界控制和观测下，对非光滑周期参考信号的输出跟踪，以及边界上的周期性干扰。 显示英文摘要

摘要： We construct two error feedback controllers for robust output tracking and disturbance rejection of a regular linear system with nonsmooth reference and disturbance signals. We show that for sufficiently smooth signals the output converges to the reference at a rate that depends on the behaviour of the transfer function of the plant on the imaginary axis. In addition, we construct a controller that can be designed to achieve robustness with respect to a given class of uncertainties in the system, and present a novel controller structure for output tracking and disturbance rejection without the robustness requirement. We also generalize the internal model principle for regular linear systems with boundary disturbance and for controllers with unbounded input and output operators. The construction of controllers is illustrated with an example where we consider output tracking of a nonsmooth periodic reference signal for a two-dimensional heat equation with boundary control and observation, and with periodic disturbances on the boundary.