Category: Publications

@inproceedings{SutrTren21,

title = {Observability of Switched Linear Singular System in Discrete Time: Single Switch Case},

author = {Sutrisno and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2021/04/Preprint-ST210406.pdf, Preprint},

year  = {2021},

date = {2021-06-29},

booktitle = {Proc. European Control Conference (ECC21)},

address = {Rotterdam, Netherlands},

abstract = {In this paper, we investigate the observability of singular linear switched systems in discrete time. As a preliminary study, we restrict ourselves to systems with a single switch switching signal, i.e. the system switches from one mode to another mode at a certain switching time. We provide two necessary and sufficient conditions for the observability characterization. The first condition is applied for arbitrary switching time and the second one is for switching times that are far enough from the initial time and the final time of observation. These two conditions explicitly contain the switching time variable that indicates that in general, the observability is dependent on the switching time. However, under some sufficient conditions we provide, the observability will not depend on the switching time anymore. Furthermore, the observability of systems with two-dimensional states is inde- pendent of the switching time. In addition, from the example we discussed, an observable switched system can be built from two unobservable modes and different mode sequences may produce different observability property; in particular, swapping the mode sequence may destroy observability.},

note = {to appear},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{HossTren21,

title = {Minimal realization for linear switched systems with a single switch},

author = {Sumon Hossain and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2021/04/Preprint-HT210406.pdf, Preprint},

year  = {2021},

date = {2021-06-29},

booktitle = {Proc. European Control Conference (ECC21)},

address = {Rotterdam, Netherlands},

abstract = {We discuss the problem of minimal realization for linear switched systems with a given switching signal and present some preliminary results for the single switch case. The key idea is to extend the reachable subspace of the second mode to include nonzero initial values (resulting from the first mode) and also extend the observable subspace of the first mode by taking information from the second mode into account. We provide some simple examples to illustrate the approach.},

note = {to appear},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@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/2021/04/Preprint-CT210406.pdf, Preprint},

year  = {2021},

date = {2021-04-06},

booktitle = {Proceedings of the MTNS 2020/21},

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 = {to appear},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{ChenTren21c,

title = {An approximation for nonlinear differential-algebraic equations via singular perturbation theory},

author = {Yahao Chen and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2021/03/Preprint-CT210326.pdf, Preprint},

year  = {2021},

date = {2021-03-26},

booktitle = {Proceedings of 7th IFAC Conference on Analysis and Design of Hybrid Systems (ADHS21)},

address = {Brussels, Belgium},

organization = {IFAC},

abstract = {In this paper, we study the jumps of nonlinear DAEs caused by inconsistent initial values. First, we propose a simple normal form called the index-1 nonlinear Weierstrass form (INWF) for nonlinear DAEs. Then we generalize the notion of consistency projector introduced in Liberzon and Trenn (2009) for linear DAEs to the nonlinear case. By an example, we compare our proposed nonlinear consistency projectors with two existing consistent initialization methods (one is from the paper Liberzon and Trenn (2012) and the other is given by a MATLAB function) to show that the two existing methods are not coordinate-free, i.e., the consistent points calculated by the two methods are not invariant under nonlinear coordinates transformations. Next we propose a singular perturbed system approximation for nonlinear DAEs, which is an ordinary differential equation (ODE) with a small perturbation parameter and we show that the solutions of the proposed perturbation system approximate both the jumps resulting from the nonlinear consistency projectors and the C1-solutions of the DAE. At last, we use a numerical simulation of a nonlinear DAE model arising from an electric circuit to illustrate the effectiveness of the proposed singular perturbed system approximation of DAEs.},

note = {to appear},

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},

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{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},

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}

}