Sensor and Actuator Placement for Linear Systems Based on $H_{2}$ and $H_{infty}$ Optimization
Sensor and Actuator Placement for Linear Systems Based on $H_{2}$ and $H_{infty}$ Optimization
复制标题
基于 $H_{2}$ 和 $H_{infty}$ 优化的线性系统传感器和执行器放置
DOI：
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发表时间：
2014
影响因子：
6.8
通讯作者：
P. Wolfrum
中科院分区：
文献类型：
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作者：
Ulrich Münz;Maximilian Pfister;P. Wolfrum
针对线性离散时间系统，提出了基于H<SUB>2</SUB>和H<SUB>∞</SUB>优化的传感器和执行器配置算法。对于传感器配置，我们设计了一种观测器，使误差动态的H<SUB>2</SUB>范数和传感器数目同时最小化。对于执行器配置，我们设计了一种状态反馈控制器，使闭环系统的H<SUB>∞</SUB>范数和执行器数目同时最小。对于基于H<sup>2</sup>或H<sup>∞</sup>优化的连续时间或离散时间线性系统，用于状态反馈设计的执行器布置或用于观测器设计的传感器布置的任何其他组合都可以从这些结果中得到。在这两种情况下，传感器或执行器的数目被表示为观测器或控制器增益矩阵的ℓ<SUB>0</SUB>范数。然后，该ℓ<sup>0</sup>范数被放宽为加权的ℓ<sup>1</sup>范数，以获得迭代凸优化问题。作为应用实例，我们使用传感器布局算法在电网中布置对H<SUB>2</SUB>性能影响最大的相位测量单元。
Sensor and actuator placement algorithms are developed for linear discrete-time systems based on H<sub>2</sub> and H<sub>∞</sub> optimization. For sensor placement, we design an observer that minimizes the H<sub>2</sub> norm of the error dynamics and the number of sensors at the same time. For actuator placement, we design a state feedback controller that minimizes the H<sub>∞</sub> norm of the closed-loop system and the number of actuators at the same time. Any other combination of actuator placement for state-feedback design or sensor placement for observer design for continuous- time or discrete-time linear systems based on H<sub>2</sub> or H<sub>∞</sub> optimization can be derived from these results. In both presented cases, the number of sensors or actuators is formulated as the ℓ<sub>0</sub> norm of the observer or controller gain matrix. This ℓ<sub>0</sub> norm is then relaxed to a weighted ℓ<sub>1</sub> norm in order to obtain an iterative convex optimization problem. As an application example, we use the sensor placement algorithm to place phase measurement units with maximal impact on the H<sub>2</sub> performance in a power grid.