The chair of Prof. Bajcinca focuses on research of modern methods and advanced applications of control and system theory, involving three main pillars: cyber-physical systems, complex dynamical systems and machine learning. Through networking with a large number of national and international research, academic and industrial partners, funding projects with exotic and highly interesting tasks regarding model-based and data-driven control have been acquired on a regular basis. The research work is supported with an excellent laboratory equipment and high-performance computation in the areas of autonomous systems, robotics and energy systems, which is continuously being further developed.

https://www.mv.uni-kl.de/mec/home.
 

Large-scale systems constructed as interconnections of a number of smaller components, each of which has the output affecting the dynamics of its neighbours, have many engineering applications: power networks, computer and telecommunications networks, economic systems and multi-agent systems, logistics, vehicle platooning, robots, chemical, and aerospace engineering, etc. Due to the physical restrictions on information exchange among subsystems, as well as due to  the complexity of possible centralized control of networks with a large number of nodes, it is often preferred to design a decentralized or distributed controller which depends only on local information available from every node and probably from its closest neighbours.

Many works focus on various conditions of stability of large-scale networks obtained within the general theory of input-to-state stability (ISS), small-gain theorems, and on their applications to decentralized or distributed control of complex networks. On the other hand, design of adaptive controllers for large-scale networks requires revision of the above-mentioned algorithms in the same way as any problem of adaptive control of a single isolated agent is a generalization of the corresponding classical problem of stabilization for a system without uncertainties. For instance, since the second Lyapunov method is replaced with LaSalle principle or Barbalat’s lemma in the case of adaptive control, the design of a common Lyapunov function for the entire network by small-gain approach differs widely from its classical version for interconnected systems with known dynamics. Therefore, decentralized and distributed adaptive control of large-scale networks is a difficult and challenging problem especially in the case when the number of subsystems is not limited, interconnection topologies are arbitrary, and the dynamics of each subsystem is nonlinear.
 

The goal of this project is to develop new algorithms of decentralized and distributed adaptive control for large-scale networks of nonlinear control systems. As the first stage, the aim is to extend the existing theory of input-to-state stability of nonlinear systems in order to to make it applicable to decentralized and distributed adaptive control of networks and multi-agent systems with the emphasis on the case when the set of nodes is not limited and is not a-priori known. The latter may include not only generalizations of the existing small-gain theorems, but also updates of the existing characterizations of the input-to-state stability, especially when dealing with trajectory-based small gain theorems. At the second stage, we need to redesign the existing algorithms of adaptive control for complex networks, and to provide a mathematically strict proof that each proposed method indeed provides the convergence in the corresponding state space. 

The research compiles from the following list of tasks.

• To develop new model-based algorithms of decentralized and distributed adaptive control of large-scale networks and multi-agent systems 
• As the first stage of the previous item, one needs to redesign the corresponding existing methods of the theory of input-to-state stability
• To develop new mathematical theories which provide a fundamental background for the efficiency of the above-mentioned algorithms
• To demonstrate the efficiency of the obtained new methods in engineering applications in power systems and smart grids
   

• Above average university degree in applied mathematics, automatic control, mechanical or electrical engineering or related area is expected.
• Knowledge in stability theory, nonlinear control, differential equations, and dynamical systems is expected.
• Organisational and team work skills with scientific collaborators from different disciplines.
• Knowledge of at least one programming language: Matlab/Python/C++ and/or experience in numerical simulation is an advantage.
• Proficiency in English is essential. Knowing German is an advantage.
• Highly motivated, eager to work within a team or independently.
   

• Payment according to TV-L E13 with an initial one-year time limit
• The possibility to do a PhD and to teach is given in case of scientific aptitude
• TUK strongly encourages qualified female academics to apply
• Severely disabled persons will be given preference in the case of appropriate suitability (please enclose proof)
• Electronic application is preferred. Please attach only one coherent PDF.

You can expect an interesting, diversified and responsible task within a young, highly motivated and interdisciplinary team of a growing chair with great personal creativity freedom.

Prof. Dr.-Ing. Naim Bajcinca
Phone: +49 (0)631/205-3230
Mobile: +49 (0)172/614-8209
Fax:  +49 (0)631/205-4201
Email: mec-apps(at)mv.uni-kl.de

Large-scale networks
Robust control
Adaptive control
Input-to-state stability
 

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31. October 2023

Immediate