Category: Submitted

@inproceedings{ChenTren21b,

title = {On geometric and differentiation index of nonlinear differential-algebraic equations},

author = {Yahao Chen and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2022/03/ChenTren21b.pdf, Paper},

doi = {10.1016/j.ifacol.2021.06.075},

year  = {2021},

date = {2021-04-06},

urldate = {2021-04-06},

booktitle = {IFAC-PapersOnLine (Proceedings of the MTNS 2020/21)},

volume = {54},

number = {9},

pages = {186-191},

publisher = {Elsevier},

organization = {IFAC},

abstract = {We discuss two notions of index, i.e., the geometric index and the differentiation index for nonlinear differential-algebraic equations (DAEs). First, we analyze solutions of nonlinear DAEs by revising a geometric reduction method (see e.g. Rabier and Rheinboldt (2002),Riaza (2008)). Then we show that although both of the geometric index and the differentiation index serve as a measure of difficulties for solving DAEs, they are actually related to the existence and uniqueness of solutions in a different manner. It is claimed in (Campbell and Gear, 1995) that the two indices coincide when sufficient smoothness and assumptions are satisfied, we elaborate this claim and show that the two indices indeed coincide if and only if a condition of uniqueness of solutions is satisfied (under certain constant rank assumptions). Finally, an example of a pendulum system is used to illustrate our results on the two indices.},

note = {open access},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{WijnJeen20,

title = {On stabilizability of switched differential algebraic equations},

author = {Paul Wijnbergen and Mark Jeeninga and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2021/06/WijnJeen20.pdf, Paper},

doi = {10.1016/j.ifacol.2020.12.2580},

year  = {2020},

date = {2020-07-06},

booktitle = {IFAC-PapersOnLine 53-2},

pages = {4304-4309},

abstract = {This paper considers stabilizability of switched differential algebraic equations (DAEs). We first introduce the notion of interval stabilizability and show that under a certain uniformity assumption, stabilizability can be concluded from interval stabilizability. A geometric approach is taken to find necessary and sufficient conditions for interval stabilizability. This geometric approach can also be utilized to derive a novel characterization of controllability.},

note = {Proc. IFAC World Congress 2020, Berlin, Germany. Open access.},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{HossTren20a,

title = {A time-varying Gramian based model reduction approach for Linear Switched Systems},

author = {Sumon Hossain and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2021/06/HossTren20a.pdf, Paper (open access)},

doi = {10.1016/j.ifacol.2020.12.1580},

year  = {2020},

date = {2020-07-05},

urldate = {2020-07-05},

booktitle = {IFAC PapersOnline 53-2},

pages = {5629-5634},

abstract = {We propose a model reduction approach for switched linear system based on a balanced truncation reduction method for linear time-varying systems. The key idea is to approximate the piecewise-constant coefficient matrices with continuous time-varying coefficients and then apply available balance truncation methods for (continuous) time-varying systems. The proposed method is illustrated with a low dimensional academic example.},

note = {Proc. IFAC World Congress 2020, Berlin, Germany. Open access.},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{WijnTren20,

title = {Impulse controllability of switched differential-algebraic equations},

author = {Paul Wijnbergen and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2020/02/Preprint-WT200204.pdf, Preprint},

doi = {10.23919/ECC51009.2020.9143713},

year  = {2020},

date = {2020-05-15},

booktitle = {Proc. European Control Conference (ECC 2020)},

pages = {1561-1566},

address = {Saint Petersburg, Russia},

abstract = {This paper addresses impulse controllability of switched DAEs on a finite interval. First we present a forward approach where we define certain subspaces forward in time. These subpsaces are then used to provide a sufficient condition for impulse controllability. In order to obtain a full characterization we present afterwards a backward approach, where a sequence of subspaces is defined backwards in time. With the help of the last element of this backward sequence, we are able to fully characterize impulse controllability. All results are geometric results and thus independent of a coordinate system.},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{LeeBerg20,

title = {Utility of edge-wise funnel coupling for asymptotically solving distributed consensus optimization},

author = {Jin Gyu Lee and Thomas Berger and Stephan Trenn and Hyungbo Shim},

url = {https://stephantrenn.net/wp-content/uploads/2020/02/Preprint-LBTS200204.pdf, Preprint},

doi = {10.23919/ECC51009.2020.9143983},

year  = {2020},

date = {2020-05-14},

booktitle = {Proc. European Control Conference (ECC 2020)},

pages = {911-916},

address = {Saint Petersburg, Russia},

abstract = {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.},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{LeeBerg20,

title = {Utility of edge-wise funnel coupling for asymptotically solving distributed consensus optimization},

author = {Jin Gyu Lee and Thomas Berger and Stephan Trenn and Hyungbo Shim},

url = {https://stephantrenn.net/wp-content/uploads/2020/02/Preprint-LBTS200204.pdf, Preprint},

doi = {10.23919/ECC51009.2020.9143983},

year  = {2020},

date = {2020-05-14},

booktitle = {Proc. European Control Conference (ECC 2020)},

pages = {911-916},

address = {Saint Petersburg, Russia},

abstract = {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.},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{LeeTren19,

title = {Asymptotic tracking via funnel control},

author = {Jin Gyu Lee and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2019/03/Preprint-LT190910.pdf, Preprint},

doi = {10.1109/CDC40024.2019.9030274},

year  = {2019},

date = {2019-12-13},

booktitle = {Proc. 58th IEEE Conf. Decision Control (CDC) 2019},

pages = {4228-4233},

address = {Nice, France},

abstract = {Funnel control is a powerful and simple method to solve the output tracking problem without the need of a good system model, without identification and without knowledge how the reference signal is produced, but transient behavior as well as arbitrary good accuracy can be guaranteed. Until recently, it was believed that the price to pay for these very nice properties is that only practical tracking and not asymptotic tracking can be achieved. Surprisingly, this is not true! We will prove that funnel control – without any further assumptions – can achieve asymptotic tracking.},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{TrenUnge19,

title = {Delay regularity of differential-algebraic equations},

author = {Stephan Trenn and Benjamin Unger},

url = {https://stephantrenn.net/wp-content/uploads/2019/03/Preprint-TU190910.pdf, Preprint},

doi = {10.1109/CDC40024.2019.9030146},

year  = {2019},

date = {2019-12-12},

booktitle = {Proc. 58th IEEE Conf. Decision Control (CDC) 2019},

pages = {989-994},

address = {Nice, France},

abstract = {We study linear time-invariant delay differential-algebraic equations (DDAEs). Such equations can arise if a feedback controller is applied to a descriptor system and the controller requires some time to measure the state and to compute the feedback resulting in the time-delay. We present an existence and uniqueness result for DDAEs within the space of piecewise-smooth distributions and an algorithm to determine whether a DDAE is delay-regular.},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{AnhLinh19,

title = {The one-step-map for switched singular systems in discrete-time},

author = {Pham Ky Anh and Pham Thi Linh and Do Duc Thuan and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2019/03/Preprint-ALTT190910.pdf, Preprint},

doi = {10.1109/CDC40024.2019.9030154},

year  = {2019},

date = {2019-12-11},

urldate = {2019-12-11},

booktitle = {Proc. 58th IEEE Conf. Decision Control (CDC) 2019},

pages = {605-610},

address = {Nice, France},

abstract = {We study switched singular systems in discrete time and first highlight that in contrast to continuous time regularity of the corresponding matrix pairs is not sufficient to ensure a solution behavior which is causal with respect to the switching signal. With a suitable index-1 assumption for the whole switched system, we are able to define a one-step- map which can be used to provide explicit solution formulas for general switching signals.},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{GrosTren18,

title = {Switch induced instabilities for stable power system DAE models},

author = {Tjorben B. Gross and Stephan Trenn and Andreas Wirsen},

url = {https://stephantrenn.net/wp-content/uploads/2018/04/Preprint-GTW180413.pdf, Preprint},

doi = {10.1016/j.ifacol.2018.08.022},

year  = {2018},

date = {2018-07-11},

booktitle = {IFAC-PapersOnLine},

journal = {IFAC-PapersOnLine},

volume = {51},

number = {16},

pages = {127-132},

abstract = {It is well known that for switched systems the overall dynamics can be unstable despite stability of all individual modes. We show that this phenoma can indeed occur for a linearized DAE model of power grids. By making certain topological assumptions on the power grid, we can ensure stability under arbitrary switching.},

note = {Proc. IFAC Conf. Analysis Design Hybrid Systems (ADHS 2018)},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}