This paper is devoted to the design of an optimal stabilizing compensator for a boundary control distributed parameter system that is described by a set of hyperbolic partial differential equations (PDEs). The standard reformulation of a boundary control system is adopted here to write the system under a regular infinite-dimensional linear system. A finite-dimensional boundary optimal controller is designed based on the linear quadratic technique and the corresponding operator Riccati equation. On the other hand, a Luenberger observer is designed based on the duality between the control and the estimation problems. Combination of the designed controller and observer is performed to construct a stabilizing compensator. A case study of tubular cracking chemical reactor is used to test the performances of the developed algorithm.

本文致力于边界控制分布参数系统的最佳稳定补偿器的设计，该系统由一组双曲型偏微分方程（PDE）来描述。这里采用边界控制系统的标准格式，将系统写成规则的无限维线性系统。基于线性二次技术和相应的算子Riccati方程设计了一个有限维边界最优控制器。另一方面，基于控制问题和估计问题之间的对偶性，设计了Luenberger观测器。执行所设计的控制器和观察器的组合以构造稳定补偿器。以管式裂解化学反应器为例，测试了该算法的性能。