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Trenn, Stephan; Shim, Hyungbo Edge-wise funnel output synchronization of heterogeneous agents with relative degree one Unpublished 2023, (submitted). Abstract | Links | BibTeX | Tags: funnel-control, networks, nonlinear, relative-degree, synchronization @unpublished{LeeBerg23pp, When a group of heterogeneous node dynamics are diffusively coupled with a high coupling gain, the group exhibits a collective emergent behavior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. |

## 2022 |

Yin, Hao; Jayawardhana, Bayu; Trenn, Stephan On contraction analysis of switched systems with mixed contracting-noncontracting modes via mode-dependent average dwell time Miscellaneous Book of Abstracts - 41th Benelux Meeting on Systems and Control, 2022. Links | BibTeX | Tags: LMIs, Lyapunov, stability, switched-systems, synchronization @misc{YinJaya22m, |

Lee, Jin Gyu; Trenn, Stephan; Shim, Hyungbo Synchronization with prescribed transient behavior: Heterogeneous multi-agent systems under funnel coupling Journal Article In: Automatica, vol. 141, no. 110276, pp. 13, 2022, (open access). Abstract | Links | BibTeX | Tags: funnel-control, nonlinear, synchronization @article{LeeTren22, In this paper, we introduce a nonlinear time-varying coupling law, which can be designed in a fully decentralized manner and achieves approximate synchronization with arbitrary precision, under only mild assumptions on the individual vector fields and the underlying (undirected) graph structure. The proposed coupling law is motivated by the so-called funnel control method studied in adaptive control under the observation that arbitrary precision synchronization can be achieved for heterogeneous multi-agent systems by a high-gain coupling; consequently we call our novel synchronization method ‘(node-wise) funnel coupling.’ By adjusting the conventional proof technique in the funnel control study, we are even able to obtain asymptotic synchronization with the same funnel coupling law. Moreover, the emergent collective behavior that arises for a heterogeneous multi-agent system when enforcing arbitrary precision synchronization by the proposed funnel coupling law, is analyzed in this paper. In particular, we introduce a single scalar dynamics called ‘emergent dynamics’ which describes the emergent synchronized behavior of the multi-agent system under funnel coupling. Characterization of the emergent dynamics is important because, for instance, one can design the emergent dynamics first such that the solution trajectory behaves as desired, and then, provide a design guideline to each agent so that the constructed vector fields yield the desired emergent dynamics. We illustrate this idea via the example of a distributed median solver based on funnel coupling. |

## 2020 |

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. |

## 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. |

## 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. |