H2-Optimal Sensor Location

Abstract

Optimal sensor placement is an important problem with many applications; placing thermostats in rooms, installing pressure sensors in chemical columns or attaching vibration detection devices to structures are just a few of the examples. Frequently, this placement problem is encountered while noise is present. The H_2-optimal control is a strategy designed for systems that have exogenous disturbing inputs. Therefore, one approach for the optimal sensor location problem is to combine it with the H_2-optimal control. In this work the H_2-optimal control is explained and combined with the sensor placement problem to create the H_2-optimal sensor location problem. The problem is examined for the one-dimensional beam equation and the two-dimensional diffusion equation in an L-shaped region. The optimal sensor location is calculated numerically for both models and multiple scenarios are considered where the location of the disturbance and the actuator are varied. The effect of different model parameters such as the weight of the state and the disturbance are investigated. The results show that the optimal sensor location tends to be close to the disturbance location.