Analysis and control of networked dynamical systems
Recent achievements in the engineering sciences and in computer and communication technology lead to more complex and largescale cyberphysical systems comprising multiple dynamical systems interacting with each other. Some of the most prominent examples are smart grids, automated highway systems, and smart factories (Industry 4.0). In order to handle, analyze, and design such network systems, a systems theoretic framework is required and appropriate control methods need to be developed.
With our research, we contribute to the development of a control theory for network systems. We investigate the interplay of the dynamics of the individual systems, the coupling between the systems and their communication protocols. The goal is to derive structural conditions and develop distributed control laws guaranteeing consensus, synchronization, stability, and satisfying desired performance criteria.
 Contact Persons: Frank Allgöwer, Christian Ebenbauer, Steffen Linsenmayer, Simon Michalowsky, Philipp Wenzelburger
Please find below all our recent research fields at the Institute for Systems Theory and Automatic Control referring to Networked Dynamical Systems.
Table of content
 Optimization of the Communication System for Networked Control Systems
 Control theoretic foundations for Industrie 4.0
 Practical Synchronization
 Distributed convex optimization over directed graphs
 Cooperative Estimation for LargeScale Systems and Heterogeneous MultiAgent Systems
 Distributed and Cooperative Control of Heterogeneous MultiAgent Systems
 Distributed Optimization in PeertoPeer Networks
 PassivityBased Control of Network Systems
 Synchronization of Oscillators
Optimization of the Communication System for Networked Control Systems
Networked Control Systems are systems where the control loop is closed over a packet based communication system. Unfortunately, such a packet based communication system introduces packet loss and delay. Consequently, in the field of Networked Control Systems, the challenge is to find a controller that stabilizes the system despite packet loss and delay.
At the IST, we work towards having a more detailed view of the communication system and taking these details into account when designing the controller. This research direction within the field of Networked Control Systems is motivated by the observation that the communication system is build by engineers too, i.e., it can be optimized to support the control specific requirements. When designing a communication system, there are many tradeoffs, e.g., between the offered load, its traffic pattern, and the resulting loss and delay. Hence, we work on methods to take these tradeoffs into account when designing the controller.
Contact Person: Frank Allgöwer, Steffen Linsenmayer
 Publications:
 R. Blind and F. Allgöwer.
On timetriggered and eventbased control of integrator systems over a shared communication system.
Mathematics of Control, Signals, and Systems, Vol. 25, No. 4, pp 517557, 2013.  R. Blind and F. Allgöwer.
On the Optimization of the Transport Layer for Networked Control Systems.
atAutomatisierungstechnik, Vol. 61, No. 7, pp. 495505, 2013.  R. Blind and F. Allgöwer.
On the Joint Design of Controller and Routing for Networked Control Systems.
In Proc. of the 4th IFAC Workshop on Distributed Estimation and Control in Networked Systems (NecSys), Koblenz, Germany, 2013, pp. 240246.  S. Linsenmayer, D. V. Dimarogonas, and F. Allgöwer. A nonmonotonic approach to periodic eventtriggered control with packet loss. In Proc. of the 55th IEEE Conference on Decision and Control (CDC), Las Vegas, NV, USA, 2016, pp. 507  512..
 Cooperations:
 Ben Carabelli, Institute of Parallel and Distributed Systems, University of Stuttgart
 Dimos V. Dimarogonas , KTH Royal Institute of Technology, Stockholm, Sweden
Control theoretic foundations for Industrie 4.0
In "Industrie 4.0", the focus is on optimizing the interconnection of devices and plants in order to improve the efficiency and productivity of factories. With today‘s advancements of technologies, mainly in information and communication technology, computational units and network interfaces can be integrated in more and more machines. This allows for novel structures in the factories of the future. The longterm goal is to create flexible structures which can adapt to required and unforeseen changes.
At first glance it may seem that the many visions developed during the project Industrie 4.0 do not require control theoretic considerations. Yet it is not clear whether existing control concepts can cope with the flexible structures of the arising industrial networks. Therefore, we analyze the concepts of Industrie 4.0 and derive mathematical models which can be analyzed using methods from systems and control theory. Based on a deeper understanding of the underlying problems, the scientific foundation for the discussion on Industrie 4.0 can be enriched and control theoretic methods enhanced to clear the way to the smart factory of the future.
 Contact Persons: Frank Allgöwer, Philipp Wenzelburger
 Publications:
 Kim D. Listmann, Philipp Wenzelburger und Frank Allgöwer
Industrie 4.0 – (R)evolution ohne Regelungstechnik?
at – Automatisierungstechnik, Vol. 64, 2016  Kim D. Listmann, Philipp Wenzelburger und Frank Allgöwer
Industrie 4.0  (R)evolution without Control Technologies?
Journal of The Society of Instrument and Control Engineers, Vol. 55, 2016
 Cooperation:

Kim D. Listmann, ABB AG, Forschungszentrum Deutschland
Practical Synchronization
In synchronization problems, one is usually concerned with sufficient conditions for coupled differential equations to converge to the socalled synchronization manifold. When these sufficient conditions are not met, then, usually, the systems converge to a neighborhood of the synchronization manifold. In practical synchronization, we are able to render this neighborhood arbitrarily small. This applies when the systems are subject to parameter uncertainties, disturbances, or drift.
 Contact Person: Frank Allgöwer, Jan Maximilian Montenbruck
 Publications:
 J. M. Montenbruck, M. Bürger, and F. Allgöwer.
Practical Cluster Synchronization of Heterogeneous Systems on Graphs with Acyclic Topology.
In Proc. of the 52nd IEEE Conference on Decision and Control (CDC), Florence, Italy, 2013, pp. 692697.  J. M. Montenbruck, G. S. Seyboth, and F. Allgöwer.
Practical and Robust Synchronization of Systems with Additive Linear Uncertainties.
In Proc. of the 9th IFAC Symposium on Nonlinear Control Systems, Toulouse, France, 2013, pp. 743748.
Distributed convex optimization over directed graphs
Solving optimization problems using a group of agents, each capable of interchanging information over a communication network, has become an important area of research. Distributed optimization problems arise in many applications such as optimal power dispatch problems in Smart Grids, distributed Machine Learning or formation control of small mobile robots.
Existing algorithms solving these problems often have quite limiting requirements on the problem class as well as the communication structure, e.g., consensustype problems or undirected information flow. In our research we focus on the development of new approaches to distributed optimization, both in continuous as well as discretetime, which are applicable to a large class of constrained optimization problems under mild assumptions on the underlying communication network as well as the problem structure. In particular, we employ primaldual algorithms for centralized convex optimization and use Lie bracket approximation techniques to derive distributed approximations thereof.
 Contact Person: Christian Ebenbauer, Simon Michalowsky
 Publications:
 C. Ebenbauer, S. Michalowsky, V. Grushkovskaya, B. Gharesifard.
Distributed Optimization over directed graphs with the help of Lie brackets.
In Proc. of the 20th IFAC World Congress, Toulouse, France, 2017, pp. 1590815913.
 Cooperation:
 Bahman Gharesifard, Queen's University, Kingston, ON, Canada.
Cooperative Estimation for LargeScale Systems and Heterogeneous MultiAgent Systems
Decentralized and distributed estimators have gained attention since decentralized control appeared in control theory in the 1970s. In a distributed estimator setup, multiple estimators create an estimate of the system’s state, while cooperating with each other. As a result, cooperation reduces the effects of model and measurement disturbances. Also, the situations are not uncommon where every single estimator is unable to obtain an estimate of the state on its own and cooperation becomes an essential prerequisite.
Our project deals with the development of a new framework for distributed state estimation for largescale systems. In largescale systems, scalability of the system is important, i.e. the dimension of the local estimators should not increase with the total size of the system. For instance, this is relevant for multiagent systems, where the agents are not able to perform selfmeasurement, but only receive relative information. Our goal is to design a distributed estimation setup, where local estimators only reproduce local state variables and their complexity does not grow with the total size of the system. Cooperation between the local estimators will be crucial due to possible lack of local detectability, therefore calling this setup Cooperative Estimation. Moreover, we investigate on estimator performance with respect to model and measurement disturbances.
 Contact Persons: Frank Allgöwer, Jingbo Wu
 Publications:

Jingbo Wu, and Frank Allgöwer.
Verteilte Ausgangsregelung linearer Multiagenten Systeme mit gekoppelten Messgrößen.
ATAutomatisierungstechnik, vol. 64/8, pp. 645657, 2016. 
JingboWu, Valery Ugrinovskii, and Frank Allgöwer.
Cooperative Hinfinityestimation for largescale interconnected linear systems.
In Proc. American Control Conference, pages 21192124, Chicago, IL, USA, 2015. DOI: 10.1109/ACC.2015.7171046. 
Jingbo Wu, Li Li, Valery Ugrinovskii, and Frank Allgöwer.
Distributed filter design for cooperative Hinfinitytype estimation.
In Proc. IEEE Conference on Control Applications (CCA), pages 13731378, Sydney, Australia, 2015. DOI: 10.1109/CCA.2015.7320803.
 Cooperation:
 Valery Ugrinovskii, School of Information Technology and Electrical Engineering, University of New South Wales at ADFA Australian Defence Force Academy, Canberra, Australia
Distributed and Cooperative Control of Heterogeneous MultiAgent Systems
This research project is dedicated to the study of cooperative control problems in groups of dynamical agents. In a variety of modern manmade systems, it is desirable to synthesize a cooperative behavior among individual dynamical agents by distributed control laws. Examples include multivehicle coordination or formation flight problems, robot cooperation in production lines, as well as power balancing in microgrids, and many more. Even though this area has become one of the major research fields within automatic control over the past decade, there are still many open questions and unsolved problems. In this project, the focus is on heterogeneous multiagent systems, i.e., cooperative control problems in groups of agents with nonidentical dynamics.
This project shall contribute to the development of a cooperative control theory for heterogeneous multiagent systems consisting of nonidentical dynamical agents. The goal is to reveal and explain fundamental effects of nonidentical agent dynamics on the behavior of a distributed system and to develop suitable analysis and synthesis methods for such multiagent coordination problems.
 Contact Person: Frank Allgöwer, Georg Seyboth
 Publications:
 G. Seyboth and F. Allgöwer.
Output Synchronization of Linear Multiagent Systems under Constant Disturbances via Distributed Integral Action. In Proc. of the American Control Conference (ACC), 2015. Chicago, IL, USA, 2015, pp. 6267.  G. Seyboth, D.V. Dimarogonas, K.H. Johansson, P. Frasca, and F. Allgöwer.
On Robust Synchronization of Heterogeneous Linear MultiAgent Systems with Static Couplings.
Automatica 53, 2015, pages 392399.  G. Seyboth, J. Wu, J. Qin, C. Yu, and F. Allgöwer.
Collective Circular Motion of Unicycle Type Vehicles with Nonidentical Constant Velocities.
IEEE Trans. Control of Network Systems, 1(2), 2014, pages 167176.
 Cooperations:
 Dimos V. Dimarogonas and Karl H. Johansson, KTH Royal Institute of Technology, Stockholm, Sweden.
 Changbin (Brad) Yu and Jiahu Qin, ANU Australian National University, Canberra, Australia.
 Paolo Frasca, University of Twente, Enschede, The Netherlands.
 Wei Ren, University of Riverside, CA, USA.
Distributed Optimization in PeertoPeer Networks
We study and develop distributed algorithms to solve optimization problems over asynchronous and unreliable communication networks. The focus of our research is on algorithms that do not use a central memory or computational unit, but use only a peertopeer comunication. Our goal is to provide computational tools, that support a distributed decision making and control in realtime enviroments. We have developed distributed variants of Simplex and CuttingPlane methods, and we have shown the applicability of our methods to a variety of problems, including multiagent assignments, robust optimization problems or robust predictive power management in smart grids.
 Contact Person: Frank Allgöwer, Mathias Bürger
 Publications:
 M. Bürger, G. Notarstefano, and F. Allgöwer.
A Polyhedral Approximation Framework for Convex and Robust Distributed Optimization.
IEEE Transactions on Automatic Control, Vol. 59, No. 2, pp. 384395, 2014.  M. Bürger, G. Notarstefano, F. Bullo, and F. Allgöwer.
A Distributed Simplex Algorithm for Degenerate Linear Programs and MultiAgent Assignments.
Automatica, Vol. 48, No. 9, pp. 22982304, 2012.  D. Zelazo, M. Bürger, and F. Allgöwer.
A FiniteTime Dual Method for Negotiation between Dynamical Systems.
SIAM Journal on Control and Optimization, Vol. 51, No. 1, pp. 172194, 2013.
PassivityBased Control of Network Systems
Network systems are dynamical systems composed of several subsystems, which interact via the exchange of information and/or material over a network. Such network systems appear in various different fields, including cooperative robots, transportation networks, flow and distribution networks (data, gas, electricity, ...), or biological networks. We develop control and coordination algorithms for network systems using an inputoutput perspective. In particular, we use variations of the passivity concept, to design distributed controllers that ensure a reliable and optimal operation of the network systems. In addition to the synthesis aspects, our research has a strong analytic component. For example, we provide an analytic connection between classical network optimization theory and modern cooperative control. In addition, our results turned out to be useful for the analysis of complex emergent behaviors, such as cluster synchronization.
 Contact Person: Frank Allgöwer, Mathias Bürger
 Publications:
 M. Bürger, D. Zelazo, and F. Allgöwer.
Hierarchical Clustering of Dynamical Networks Using a SaddlePoint Analysis.
IEEE Transactions on Automatic Control, Vol. 58, No. 1, pp. 113124, 2013.  M. Bürger, D. Zelazo, and F. Allgöwer.
Duality and Network Theory in Passivitybased Cooperative Control.
Automatica, Vol. 50, No. 8, pp. 20512061, 2014.  M. Bürger, C. De Persis, and F. Allgöwer.
Optimal Pricing Control in Distribution Networks With Timevarying Supply and Demand.
In Proc. of the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS), Groningen, The Netherlands, 2014, pp. 584591.
Synchronization of Oscillators
Synchronization in an oscillator network describes the effect that the interaction between a set of oscillators, which are nonlinear systems with stable periodic orbits, leads to asymptotically common oscillatory dynamics for the individual oscillators. A typical example of synchronization in an engineering system is the synchronization of generators in an electrical power network. Synchronization in oscillators network can then be investigated by analyzing the stability or attractivity of specific solutions in the mathematical models. The focus of our research in this area concerns the stability analysis of synchronous solutions in specific system classes and the development of new methods to investigate synchronization with the help of Lyapunov like functions.
 Contact Person: Frank Allgöwer, Gerd Simon Schmidt
 Publications:
 G. S. Schmidt, C. Ebenbauer, and F. Allgöwer.
Synchronization conditions for Lyapunov oscillators.
In Proc. of the 49th IEEE Conference on Decision and Control (CDC), Atlanta, Georgia, USA, 2010, pp. 62306235.  G. S. Schmidt, A. Papachristodoulou, U. Münz, and F. Allgöwer.
Frequency synchronization and phase agreement in Kuramoto oscillator networks with delays.
Automatica, Vol. 48, No. 12, pp. 30083017, 2012.