Category: Publications

@inproceedings{WijnTren21b,

title = {Optimal control of DAEs with unconstrained terminal costs},

author = {Paul Wijnbergen and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2021/09/Preprint-WT210927.pdf, Preprint},

year  = {2021},

date = {2021-09-27},

urldate = {2021-09-27},

booktitle = {Proc. 60th IEEE Conf. Decision and Control (CDC 2021)},

abstract = {This paper is concerned with the linear quadratic optimal control problem for impulse controllable differential algebraic equations on a bounded half open interval. Regarding the cost functional, a general positive semi-definite weight matrix is considered in the terminal cost. It is shown that for this problem, there generally does not exist an input that minimizes the cost functional. First it is shown that the problem can be reduced to finding an input to an index-1 DAE that minimizes a different quadratic cost functional. Second, necessary and sufficient conditions in terms of matrix equations are given for the existence of an optimal control.},

note = {to appear},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{SutrTren21b,

title = {Observability and Determinability Characterizations for Linear Switched Systems in Discrete Time},

author = {Sutrisno and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2021/09/Preprint-ST210907.pdf, Preprint},

year  = {2021},

date = {2021-09-07},

urldate = {2021-09-07},

booktitle = {Proc. 60th IEEE Conf. Decision and Control (CDC 2021)},

abstract = {In this article, we study the observability and determinability for discrete-time linear switched systems. Studies for the observability for this system class are already available in literature, however, we use assume here that the switching signal is known. This leads to less conservative observability conditions (e.g. observability of each individual mode is not necessary for the overall switched system to be observable); in particular, the dependencies of observability on the switching times and the mode sequences are derived; these results are currently not available in the literature on discrete-time switched systems. In addition to observability (which is concerned with recovering the state from the initial time onwards), we also investigate the determinability which is concerned with the ability to reconstruct the state value at the end of the observation interval. We provide several simple examples to illustrate novel features not seen in the continuous time case or for unswitched systems.},

note = {to appear},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{SutrTren21a,

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},

urldate = {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}

}