Abstract
A sparse linear system constitutes a valid model for a broad range of physical systems, such as electric power networks, industrial processes, control systems or traffic models. The physical magnitudes in those systems may be directly measured by means of sensor networks that, in conjunction with data obtained from contextual and boundary constraints, allow the estimation of the state of the systems. The term observability refers to the capability of estimating the state variables of a system based on the available information. In the case of linear systems, diffierent graphical approaches were developed to address this issue. In this paper a new unified graph based technique is proposed in order to determine the observability of a sparse linear physical system or, at least, a system that can be linearized after a first order derivative, using a given sensor set. A network associated to a linear equation system is introduced, which allows addressing and solving three related problems: the characterization of those cases for which algebraic and topological observability analysis return contradictory results; the characterization of a necessary and sufficient condition for topological observability; the determination of the maximum observable subsystem in case of unobservability. Two examples illustrate the developed techniques.
Highlights
The state variables that characterize a physical system are estimated by means of the data available at any given time
Consider a sensor network consisting of 8 traffic flow meters that result in a measured variable vector z whose magnitudes might be estimated by means of a submatrix of F and the system state variables x, that is, OD-pair traffic flows, as follows:
The techniques developed in this paper were inspired by the contributions of researchers in the scope of electric power systems and generalized to other physical sparse linear systems
Summary
The state variables that characterize a physical system are estimated by means of the data available at any given time. Five examples are described below pursuing the following aims: on one hand, illustrating how observability and other related problems constitute research topics in different physical, engineering, and industrial areas, where a sensor network is designed in order to analyze a given system; on the other, showing the multiple points of view from which these issues can be addressed and, in particular, how topological and graph-based approaches were developed in some cases. Observability has been a motivation for research in traffic models in topics related to the origin/destination trip matrix estimation challenge This is the case of 10 , where the authors adapt topological techniques developed for electric power networks to this new context.
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