doc. Ing. Zdeněk Hurák, Ph.D.

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)

The goal of this doctoral research is to develop optimal (and optimization-based) control strategies for controlling the speed of rail vehicles (trains, trams, metro, etc.). Specifically, the focus will be on computing reference speed trajectories that minimize energy (fuel) consumption while taking into account various factors such as the grade profile, speed restrictions, timetables, and safety considerations (such as collision avoidance). All possible Information communicated to the onboard controller from higher levels of the transportation control system hierarchy, from other vehicles, or from roadside units, will also have to be taken into consideration, necessitating a capability to recompute the optimal trajectory online. Computational design of of feedback controllers for following such speed references by vehicles may also be part of the research. Ideally, the two phases should be integrated to avoid the classical schism between reference planning and reference following. The key knowledge base for this research will be optimal and optimization-based control, including extensions to hybrid systems (leading to mixed integer optimization) and stochastic systems (leading to stochastic optimal control and possibly even to some sort of learning control). In fact, it is in these two directions where some fundamental contributions can still be achieved. Although the research will be oriented towards achieving fundamental contributions publishable in international journals, it is motivated (and in fact even co-assigned) by our industrial partners. A joint grant has just been started with these partners, within which the successful candidate's doctoral research will be supported.