Minimal sparse observability of complex networks: application to MPSoC sensor placement and run-time thermal estimation & tracking

This paper addresses the fundamental and practically useful question of identifying a minimum set of sensors and their locations through which a large complex dynamical network system and its time-dependent states can be observed. The paper defines the minimal sparse observability problem (MSOP) and provides analytical tools with necessary and sufficient conditions to make an arbitrary complex dynamic network system completely observable. The mathematical tools are then used to develop effective algorithms to find the sparsest measurement vector that provides the ability to estimate the internal states of a complex dynamic network system from experimentally accessible outputs. The developed algorithms are further used in the design of a sparse Kalman filter (SKF) to estimate the time-dependent internal states of a linear time-invariant (LTI) dynamical network system. The approach is applied to illustrate the minimum sensor in-situ run-time thermal estimation and robust hotspot tracking for dynamic thermal management (DTM) of high performance processors and MPSoCs.