# System Identification in Dynamic Networks

Project members: | prof.dr.ir. P.M.J. Van den Hof (Paul), A.G. Dankers, MSc (Arne), dr. P.S.C. Heuberger (Peter) |
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Keywords: | System identification |

In many fields of science and engineering such as power systems, biological systems, flexible mechanical structures, economic systems, etc. it is becoming possible to collect data at various locations (or of different variables) that have dynamic interrelations i.e. form an interconnected network.

This research is focused on obtaining models using data collected from interconnected dynamic systems. The estimated models can then be used in controller design, prediction, or simulation. A block diagram of an interconnected dynamic system is shown below. Each block represents a transfer function (a dynamic relation), v's denote stochastic (unknown) disturbances, r's denote external variables (a variable that can be manipulated by the user), and w's denote internal variables. The w's are measurable variables.

Some issues that have been addressed so far in this research are:

### Consistency

How to obtain consistent estimates of a particular module of interest (say G23 in the figure) that is embedded in a dynamic network. Consistency means that as the size of the data set tends to infinite, the expected value of the estimated model tends to the dynamics of the data generating system.

### Predictor Inputs/Sensor Locations

In some applications, although it is possible to take measurements at many different locations in the network, it may be expensive to do so. Therefore, there is a motivation to use the minumum number of required measurement locations in order to estimate the dynamics of a particular module embedded in a network. Alternatively, perhaps some variables are difficult to measure, therefore it is desirable to avoid having to measure them.

Conditions have been derived that the set of measurements must satisfy in order to guarantee that it is possible to obtain consistent estimates of the module of interest. This enables the user to determine the minimum number of required measurement locations or whether or not it is possible to obtain a consistent estimate of the desired module while avoiding the use of a particular variable.