# PhD position

## Energy-based modeling, analysis and control of large-scale networks of physical systems

Mainstream approaches to control-oriented mathematical modeling of dynamical systems are based on classifying the variables as either the inputs or the outputs first, and then finding the corresponding (differential) equations that link these variables. The major disadvantage of these approaches is that modeling of complex systems that are composed of several subsystems and elements is typically very tedious. Moreover, it is also uninsightful – the interconnection structure of the system is not captured in the model, hence it cannot be further investigated.

Alternative modeling approaches proliferate in the dynamical systems modeling and simulation communities. These approaches are based on identification the coupling between the neighbor subsystems as power bonds and lead to modeling methodologies such as (power) bond graphs and port-Hamiltonian system. Related is the framework of object-oriented modeling using computer languages such as Modelica or Simscape. Modeling of interconnected systems is then as straightforward as their (physical) assembling. The major use of such mathematical models is numerical simulation. However, since the interconnection structure is explicitly captured in the model, new analysis and even (control) design techniques can be derived that exploit this information. The proposed research will focus on development of such techniques.

Practical motivation for the proposed doctoral research comes from the domain of electric batteries, in particular those for electric vehicles. Not only are such batteries realized as packs consisting of hundreds of series-parallel interconnected cells but also each cell can be modelled using equivalent circuits (containing a few RC terms). Hence a large scale network of interconnected physical systems.

The initial angle of attack for this research will be inspired by the work [1], where chains of dynamical systems are analyzed and controlled through a controller interacting with just one (boundary) system. Among other, the work offers a framework for an explanation and compensation of the wave phenomena observed in vehicular platoons [2] by interpreting it as an instance of impedance matching problem known to electrical engineers. In this project the framework based on wave and scattering descriptions will be extended to other interconnection structures than chains. Analysing also several battery-related problems within the same (or derived) framework might bring some useful insight and tools.

Literature

[1] Zdeněk Hurák. Traveling waves and scattering in control of chains. Habilitation thesis, Faculty of Electrical Engineering, Czech Technical University, Prague, Czech Republic, December 2015.

[2] Dan Martinec, Ivo Herman, Zdeněk Hurák, and Michael Šebek. Wave-absorbing vehicular platoon controller. European Journal of Control, 20(5):237-248, September 2014.