Dynamic models play a key role in many branches of science. In engineering they have a paramount role in model-based simulation, monitoring, control and optimization. The accuracy of the models is key to their subsequent use in model-based operations. With the growing spatial complexity of engineering systems, e.g., in power networks, transportation networks and industrial production systems, also referred to as cyber-physical systems of systems, there is a strong need for effective modelling tools for dynamic networks, being considered as interconnected dynamic systems, whose spatial topology may change over time.
Data-driven modelling and statistical parameter estimation are established fields for estimating models of dynamical systems on the basis of measurement data from dedicated experiments. The currently available methods, however, are limited to relatively simple structures, as open-loop or closed-loop (controlled) system configurations.
In this project we will make the fundamental step towards data-driven modelling (identification) methods for dynamic networks by developing a comprehensive theory with the target to identify local dynamical models as well as the interconnection structure of the network. We will incorporate the selection of sensing and excitation locations, data synchronization, and the optimal accuracy of estimated models in view of their use for distributed control.


A prototype dynamic network in the module framework

Identification methods for dynamic networks will become essential tools in the high-level future ICT environment for monitoring, control and optimization of these cyber-physical systems of systems, as well as in many other domains of science.

The scientific field of data-driven modelling of dynamical systems, also referred to as system identification, deals with the problem of estimating the mathematical specifications of a dynamical system on the basis of measurement data that is obtained from (possibly dedicatedly designed) experiments. It is a mature field with well established methods and tools that are available on a stand-alone basis or incorporated in industrial plant automation packages. Methods of system identification are applied in a vast amount of domains in science and engineering, ranging from mechatronics, robotics, industrial chemical processes, aerospace and communication systems, to econometrics, medical and biomedical systems, systems biology and neurosciences. While finding their roots in the domain of linear dynamical systems extensions to the nonlinear domain are being addressed extensively now, thereby connecting to related fields of e.g. machine learning and neural networks, however putting emphasis on the estimation of dynamical properties, and establishing a link with model-based control synthesis methods.

Identification and estimation problems are typically addressed in relative simple structural setups, i.e., in single- or multivariable open-loop or closed-loop (controlled) experimental situations. However driven by developments in the control of highly complex large-scale interconnected systems, as well by the need in several branches of science, to estimate structural properties of interconnected systems (cause-effect relationships, presence of feedback, network topology), there is a strong need for the development of identification and estimation techniques in large-scale interconnected dynamic networks.


Project objectives
Dynamical models play a key role in very many branches of science. They serve important purposes of simulation, diagnosis, and learning/understanding the characteristics of processes in our physical nature (biology, physics, medicine), and in the engineering domain they perform a paramount role in (model-based) simulation, fault detection, measurement, control and optimization. Classically the attention of the field of control and signal processing has been on relatively simple system configurations such as open-loop or closed-loop multivariable systems. However in many branches of science and engineering there is a need to consider more complex configurations like
(large-scale) interacting dynamic networks. The motivation for this is twofold:

– Many dynamical systems to be designed, controlled and/or optimized, show an increasing complexity, as well as a spatial interconnection structure. Typical examples are power distribution networks, robotic networks, transportation networks, etcetera. Rather than aiming at centralized techniques for controlling these interconnected systems (as would be most attractive from a classical control perspective), the need for decentralized and distributed control theory has become apparent as a means to handle the complexity.

– Many dynamical systems have an intrinsic structure, in which contributing submodels interact with eachother, as e.g., gene networks in systems biology, spatial-temporal models in flexible mechanics and fluid dynamics, neurosciences.

This development has also been recognized in a wider setting as the challenge of optimally managing and controlling cyber-physical systems of systems. Models can be built either on the basis of first-principles relations or on the basis of experimental data, or a combination of both. Data-driven modelling is particularly important for (a) effectively incorporating the emergent behaviour of systems, (b) quantifying and minimizing the effect of uncertainties, (c) adapting to time-varying behaviour, (d) accurately estimating the parameters in first-principles models and (e) possibly avoiding the time-consuming task of first principles modelling.



Therefore effective data-driven modelling tools for dynamic networks are essential ingredients for operating and controlling many of our future engineering systems.
The overall objective of this project is formulated as:

“Develop a comprehensive theory for the data-driven modelling of dynamic networks, that can address (a) the identification of dynamics and interconnection structure (topology) of local parts of the network, (b) aspects and optimal choices of sensor and actuator placements and of experiment design (c) incorporation of prior (partial) knowledge on network topology and local network dynamics and (d) the properties of identified (local) models that are relevant for model-based distributed control.”

With the increasing size and complexity of dynamic networks it becomes relevant for data-driven modelling methods to be able to focus on a particular part of the network, as identification of the global network will be too costly and out of reach. We will call this local identification. Identifying the local dynamic subsystems is one target, but additionally also identifying the network topology/structure is an important aspect to consider. Which node variables are causally connected to which other node variables, and can we detect the presence of (feedback) connections in the network? Statistical properties of the estimation procedures will typically be highly dependent on the information content of measured signals. This involves the possible choice and location of sensors and of actuators, and the possible design of dedicated excitation (probing) signals to achieve optimal model accuracy. If some modules in the network are known, through first-principles- based models or as known local controllers, this will substantially influence the modelling results, and so it has to be taken into account. Finally our objective is to make a step towards goal-oriented modelling for distributed control, by addressing the question: which (local) model properties are most important for arriving at high performance of the distributed control system (identification for distributed control).