Category: Publications

@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/2019/12/Preprint-WJT200506.pdf, Preprint},
year = {2020},
date = {2020-07-06},
booktitle = {Proc. IFAC World Congress 2020, Berlin, Germany},
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 = {to appear},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}

@inproceedings{HossTren20,
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/2019/12/Preprint-HT200505.pdf, Preprint},
year = {2020},
date = {2020-07-05},
booktitle = {Proc. IFAC World Congress 2020, Berlin, Germany},
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 = {to appear},
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},
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},
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},
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},
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},
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}
}

@inproceedings{IervTren17,
title = {Stability of piecewise affine systems through discontinuous piecewise quadratic Lyapunov functions},
author = {Raffaele Iervolino and Stephan Trenn and Francesco Vasca},
url = {https://stephantrenn.net/wp-content/uploads/2017/09/Preprint-ITV170909.pdf, Preprint},
doi = {10.1109/CDC.2017.8264551},
year = {2017},
date = {2017-12-15},
booktitle = {Proc. 56th IEEE Conf. Decis. Control},
pages = {5894 - 5899},
address = {Melbourne, Australia},
abstract = {State-dependent switched systems characterized by piecewise affine (PWA) dynamics in a polyhedral partition of the state space are considered. Sufficient conditions on the vectors fields such that the solution crosses the common boundaries of the polyhedra are expressed in terms of quadratic inequalities constrained to the polyhedra intersections. A piece- wise quadratic (PWQ) function, not necessarily continuous, is proposed as a candidate Lyapunov function (LF). The sign conditions and the negative jumps at the boundaries are expressed in terms of linear matrix inequalities (LMIs) via cone- copositivity. A sufficient condition for the asymptotic stability of the PWA system is then obtained by finding a PWQ-LF through the solution of a set LMIs. Numerical results with a conewise linear system and an opinion dynamics model show the effectiveness of the proposed approach.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}

@inproceedings{KausTren17b,
title = {Impulses in structured nonlinear switched DAEs},
author = {Rukhsana Kausar and Stephan Trenn},
url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-KT170920.pdf, Preprint},
doi = {10.1109/CDC.2017.8264125},
year = {2017},
date = {2017-12-14},
booktitle = {Proc. 56th IEEE Conf. Decis. Control},
pages = {3181 - 3186},
address = {Melbourne, Australia},
abstract = { Switched nonlinear differential algebraic equations (DAEs) occur in mathematical modeling of sudden transients in various physical phenomenons. Hence, it is important to investigate them with respect to the nature of their solutions. The few existing solvability results for switched nonlinear DAEs exclude Dirac impulses by definition; however, in many cases this is too restrictive. For example, in water distribution networks the water hammer effect can only be studied when allowing Dirac impulses in a nonlinear switched DAE description. We investigate existence and uniqueness of solutions with impulses for a general class of nonlinear switched DAEs, where we exploit a certain sparse structure of the nonlinearity.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}

@inproceedings{KustPati17b,
title = {Switch observability for a class of inhomogeneous switched DAEs},
author = {Ferdinand Küsters and Deepak Patil and Stephan Trenn},
url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-KPT170919.pdf, Preprint},
doi = {10.1109/CDC.2017.8264124},
year = {2017},
date = {2017-12-13},
booktitle = {Proc. 56th IEEE Conf. Decis. Control},
pages = {3175 - 3180},
address = {Melbourne, Australia},
abstract = {Necessary and sufficient conditions for switching time and switch observability of a class of inhomogeneous switched differential algebraic equations (DAEs) are obtained. A characterization of initial states and inputs for which switched DAEs are switch unobservable is also provided by using the zeros of an augmented system obtained by combining the output of two modes suitably.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}

@inproceedings{KustTren17b,
title = {Switch-observer for switched linear systems},
author = {Ferdinand Küsters and Stephan Trenn and Andreas Wirsen},
url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-KTW170901.pdf, Preprint},
doi = {10.1109/CDC.2017.8263903},
year = {2017},
date = {2017-12-12},
booktitle = {Proc. 56th IEEE Conf. Decis. Control},
pages = {1749 - 1754},
address = {Melbourne, Australia},
abstract = {To determine the switching signal and the state of a switched linear system, one usually requires mode observability. This requires that all individual modes are observable and that the modes are distinguishable. In theory, it allows to determine the active mode in an arbitrarily short time. If one enlarges the observation to an interval that contains a switch, both assumptions (observability of each mode and clearly distinct dynamics) can be relaxed. In [Küsters and Trenn 2017] this concept, called switch observability, was formalized. It is of particular interest for fault identification. Based on switch observability, we propose an observer. This observer combines the information obtained before and after a switching instant to determine both the state and the switching signal. It is analyzed and illustrated in an example.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}