10.25394/PGS.7436441.v1
Nathaniel T. Woodford
Robust Sensor Selection Strong Detectability
2019
Purdue University Graduate School
Control Theory
Unknown Input Observer
NP-Hard
Sensor Selection
Minimal Control
2019-01-16 15:59:17
article
https://hammer.figshare.com/articles/Robust_Sensor_Selection_Strong_Detectability/7436441
An unknown input observer provides perfect asymptotic tracking of the state of a system affected by unknown inputs. Such an observer exists (possibly requiring a delay in estimation) if and only if the system satisfies a property known as strong detectability. In this thesis, we consider the problem of selecting (at design-time) a minimum cost subset of sensors from a given set to make a given system strongly detectable. We show this problem is NP-hard even when the system is stable. Furthermore, we show it is not possible to approximate the minimum cost within a factor of log(n) in polynomial-time (unless P=NP). However, we prove if a given system (with a selected set of sensors) is already strongly detectable, finding the smallest set of additional sensors to install to obtain a zero-delay observer can be done in polynomial time. Next we consider the problem of attacking a set of deployed sensors to remove the property of strong detectability. We show finding the smallest number of sensors to remove is NP-hard. Lastly through simulations, we analyze two greedy approaches for approximating the strong detectability sensor selection problem.