Efficient constrained sensor placement for observability of linear systems via greedy algorithms

This article deals with problems related to efficient sensor placement in linear time-invariant discrete-time systems with partial state observations. The output matrix is assumed to be constrained in the sense that the set of states that each output can measure are pre-specified. Two problems are addressed assuming purely structural conditions at the level of only the interconnections between the system being known. 1) We establish that identifying the minimal number of sensors required to ensure a desired structural observability index is NP-complete. 2) We propose an efficient greedy strategy for selecting a fixed number of sensors from the given set of sensors in order to maximize the number of states structurally observable in the system. We identify a large class of systems for which both the problems are solvable in polynomial time using simple greedy algorithms to provide best approximate solutions. An illustration of the techniques developed here is given on the benchmark IEEE 118-bus power network, which has \(\sim 400\) states in its linearized model.