Below you find an interactive list of all my publications, which can be filtered by keywords, year, publication type and coauthors. There are also static lists of my books/book-chapters as well as journal-, conference-, and submitted publications.

## 2023 |

Lee, Jin Gyu; Berger, Thomas; Trenn, Stephan; Shim, Hyungbo Edge-wise funnel output synchronization of heterogeneous agents with relative degree one Unpublished 2023, (submitted). Abstract | Links | BibTeX | Tags: funnel-control, networks, nonlinear, relative-degree, synchronization @unpublished{LeeBerg23pp, When a group of heterogeneous node dynamics are diffusively coupled with a high coupling gain, the group exhibits a collective emergent behavior which is governed by a simple algebraic average of the node dynamics called the blended dynamics. This finding has been utilized for designing heterogeneous multi-agent systems by building the desired blended dynamics first and then splitting it into the node dynamics. However, to compute the magnitude of the coupling gain, each agent needs to know global information such as the number of participating nodes, the graph structure, and so on, which prevents a fully decentralized design of the node dynamics in conjunction with the coupling laws. To resolve this issue, the idea of funnel control, which is a method for adaptive gain selection, can be exploited for a node-wise coupling, but the price to pay is that the collective emergent behavior is no longer governed by a simple average of the node dynamics. Our analysis reveals that this drawback can be avoided by an edge-wise design premise, which is the idea that we present in this paper. After all, we gain benefits such as a fully decentralized design without global information, collective emergent behavior being governed by the blended dynamics, and the plug-and-play operation based on edge-wise handshaking between two nodes. |

## 2020 |

Borsche, Raul; Kocoglu, Damla; Trenn, Stephan A distributional solution framework for linear hyperbolic PDEs coupled to switched DAEs Journal Article In: Mathematics of Control, Signals, and Systems (MCSS), vol. 32, pp. 455-487, 2020, (Open Access). Abstract | Links | BibTeX | Tags: DAEs, delay, networks, open-access, PDEs, piecewise-smooth-distributions, solution-theory, switched-DAEs @article{BorsKoco20, A distributional solution framework is developed for systems consisting of linear hyperbolic partial differential equations (PDEs) and switched differential-algebraic equations (DAEs) which are coupled via boundary conditions. The unique solvability is then characterize in terms of a switched delay DAE. The theory is illustrated with an example of electric power lines modeled by the telegraph equations which are coupled via a switching transformer where simulations confirm the predicted impulsive solutions. |

Lee, Jin Gyu; Berger, Thomas; Trenn, Stephan; Shim, Hyungbo Utility of edge-wise funnel coupling for asymptotically solving distributed consensus optimization Inproceedings In: Proc. European Control Conference (ECC 2020), pp. 911-916, Saint Petersburg, Russia, 2020. Abstract | Links | BibTeX | Tags: funnel-control, networks, nonlinear, synchronization @inproceedings{LeeBerg20, A new approach to distributed consensus optimization is studied in this paper. The cost function to be minimized is a sum of local cost functions which are not necessarily convex as long as their sum is convex. This benefit is obtained from a recent observation that, with a large gain in the diffusive coupling, heterogeneous multi-agent systems behave like a single dynamical system whose vector field is simply the average of all agents' vector fields. However, design of the large coupling gain requires global information such as network structure and individual agent dynamics. In this paper, we employ a nonlinear time-varying coupling of diffusive type, which we call `edge-wise funnel coupling.' This idea is borrowed from adaptive control, which enables decentralized design of distributed optimizers without knowledge of global information. Remarkably, without a common internal model, each agent achieves asymptotic consensus to the optimal solution of the global cost. We illustrate this result by a network that asymptotically finds the least-squares solution of a linear equation in a distributed manner. |

## 2019 |

Patil, Deepak; Tesi, Pietro; Trenn, Stephan Indiscernible topological variations in DAE networks Journal Article In: Automatica, vol. 101, pp. 280-289, 2019. Abstract | Links | BibTeX | Tags: DAEs, networks, observability @article{PatiTesi19, A problem of characterizing conditions under which a topological change in a network of differential algebraic equations (DAEs) can go undetected is considered. It is shown that initial conditions for which topological changes are indiscernible belong to a generalized eigenspace shared by the nominal system and the system resulting from a topological change. A condition in terms of eigenvectors of the nominal system is derived to check for existence of possibly indiscernible topological changes. For homogenous networks this condition simplifies to the existence of an eigenvector of the Laplacian of network having equal components. Lastly, a rank condition is derived which can be used to check if a topological change preserves regularity of the nominal network. |

## 2017 |

Trenn, Stephan Edge-wise funnel synchronization Inproceedings In: PAMM - Proc. Appl. Math. Mech., pp. 821 - 822, WILEY-VCH Verlag, 2017, ISSN: 1617-7061. Abstract | Links | BibTeX | Tags: funnel-control, networks, nonlinear, synchronization @inproceedings{Tren17, Recently, it was suggested in [Shim & Trenn 2015] to use the idea of funnel control in the context of synchronization of multi-agent systems. In that approach each agent is able to measure the difference of its own state and the average state of its neighbours and this synchronization error is used in a typical funnel gain feedback law, see e.g. [Ilchmann & Ryan 2008]. Instead of considering one error signal for each node of the coupling graph (corresponding to an agent) it is also possible to consider one error signal for each edge of the graph. In contrast to the node-wise approach this edgewise funnel synchronization approach results (at least in simulations) in a predictable consensus trajectory. |

Küsters, Ferdinand; Patil, Deepak; Tesi, Pietro; Trenn, Stephan Indiscernible topological variations in DAE networks with applications to power grids Inproceedings In: Proc. 20th IFAC World Congress 2017, pp. 7333 - 7338, Toulouse, France, 2017, ISSN: 2405-8963. Abstract | Links | BibTeX | Tags: application, DAEs, networks, observability @inproceedings{KustPati17a, The ability to detect topology variations in dynamical networks defined by differential algebraic equations (DAEs) is considered. We characterize the existence of initial states, for which topological changes are indiscernible. A key feature of our characterization is the ability to verify indiscernibility just in terms of the nominal topology. We apply the results to a power grid model and also discuss the relationship to recent mode-detection results for switched DAEs. |

## 2016 |

Gross, Tjorben B.; Trenn, Stephan; Wirsen, Andreas Solvability and stability of a power system DAE model Journal Article In: Syst. Control Lett., vol. 97, pp. 12–17, 2016. Abstract | Links | BibTeX | Tags: application, DAEs, Lyapunov, networks, solution-theory, stability @article{GrosTren16, The dynamic model of a power system is the combination of the power flow equations and the dynamic description of the generators (the swing equations) resulting in a differential–algebraic equation (DAE). For general DAEs solvability is not guaranteed in general, in the linear case the coefficient matrices have to satisfy a certain regularity condition. We derive a solvability characterization for the linearized power system DAE solely in terms of the network topology. As an extension to previous result we allow for higher order generator dynamics. Furthermore, we show that any solvable power system DAE is automatically of index one, which means that it is also numerically well posed. Finally, we show that any solvable power system DAE is stable but not asymptotically stable. |

## 2015 |

Shim, Hyungbo; Trenn, Stephan A preliminary result on synchronization of heterogeneous agents via funnel control Inproceedings In: Proc. 54th IEEE Conf. Decis. Control, Osaka, Japan, pp. 2229–2234, 2015. Abstract | Links | BibTeX | Tags: CDC, funnel-control, networks, nonlinear, stability, synchronization @inproceedings{ShimTren15, We propose a new approach to achieve practical synchronization for heterogeneous agents. Our approach is based on the observation that a sufficiently large (but constant) gain for diffusive coupling leads to practical synchronization. In the classical setup of high-gain adaptive control, the funnel controller gained popularity in the last decade, because it is very simple and only structural knowledge of the underlying dynamical system is needed. We illustrate with simulations that “funnel synchronization” may be a promising approach to achieve practical synchronization of heterogeneous agents without the need to know the individual dynamics and the algebraic connectivity of the network (i.e., the second smallest eigenvalue of the Laplacian matrix). For a special case we provide a proof, but the proof for the general case is ongoing research. |

## 2014 |

Gross, Tjorben B.; Trenn, Stephan; Wirsen, Andreas Topological solvability and index characterizations for a common DAE power system model Inproceedings In: Proc. 2014 IEEE Conf. Control Applications (CCA), pp. 9–14, IEEE 2014. Abstract | Links | BibTeX | Tags: application, DAEs, networks, nonlinear, solution-theory @inproceedings{GrosTren14, For the widely-used power system model consisting of the generator swing equations and the power flow equations resulting in a system of differential algebraic equations (DAEs), we introduce a sufficient and necessary solvability condition for the linearized model. This condition is based on the topological structure of the power system. Furthermore we show sufficient conditions for the linearized DAE-system and a nonlinear version of the model to have differentiation index equal to one. |