Gradient-based optimization methods for sensor & actuator placement in LTI systems
Gradient-based optimization methods for sensor & actuator placement in LTI systems
复制标题
基于梯度的传感器优化方法
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
T. Bewley
中科院分区：
文献类型：
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作者：
C. Colburn;D. Zhang;T. Bewley
本文开发了用于计算梯度信息的有效技术，这些技术可用于优化给定精度的传感器和执行器，以有效地估计和控制无限二维线性时间流动（LTI）系统的高维离散通过伴随分析来确定梯度，从而量化了观测值和控制算子的小变化的影响。适当地适应线性二次高斯（LQG）估计/控制框架中的各种特定目标，我们与该领域的其他工作直接使用估计误差P的协方差P，而不是与Fischer Information Matrix M一起工作从某种意义上说，P-1的最佳估计值忽略了国家灾难对状态估计误差的进化的影响。在1D复杂的金茨堡 - 兰德系统中的传感器和两个执行器。
This paper develops efficient techniques for calculating gradient information which may be used to optimize the placement of sensors & actuators of a given precision for the effective estimation and control of high-dimensional discretizations of infinite-dimensional linear time-invariant (LTI) systems. The necessary gradients are determined in this setting via adjoint analyses which quantify the effects of small variations of the observation and control operators. The approach can be modified appropriately to fit a variety of specific objectives within the Linear Quadratic Gaussian (LQG) estimation/control framework. Unlike other work in this area, we work directly with the covariance of the estimation error P, rather than working with the Fischer information matrix M, which is, in a sense, a best-case estimate of P−1 that neglects the impact of the state disturbances on the evolution of the state estimation error. The method is tested by optimizing the placement of two sensors and two actuators in a 1D complex Ginzburg-Landau system.