Category: Publications

@inproceedings{ChenTren22b,

title = {Stability analysis of switched nonlinear differential-algebraic equations via nonlinear Weierstrass form},

author = {Yahao Chen and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2022/03/Preprint-CT220329.pdf, Preprint},

doi = {10.23919/ECC55457.2022.9838148},

year  = {2022},

date = {2022-07-12},

urldate = {2022-07-12},

booktitle = {Proceedings of the 2022 European Control Conference (ECC)},

pages = {1091-1096},

address = {London},

abstract = {In this paper, we propose some sufficient conditions for checking the asymptotic stability of switched nonlinear differential-algebraic equations (DAEs) under arbitrary switch- ing signal. We assume that each model of a given switched DAE is externally equivalent to a nonlinear Weierstrass form. With the help of this form, we can define nonlinear consistency projectors and jump-flow solutions for switched nonlinear DAEs. Then we use a different approach from the paper [12] to study the stability of switched DAEs via a novel notion called the jump-flow explicitation, which attaches a nonlinear control system to a given nonlinear DAE and can be used to simplify the common Lyapunov function conditions for both the flow and the jump dynamics of switched nonlinear DAEs. At last, a numerical example is given to illustrate how to check the stability of a switched nonlinear DAE by constructing a common Lyapunov function.

},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{MostTren22b,

title = {An averaged model for switched systems with state jumps applicable for PWM descriptor systems},

author = {Elisa Mostacciuolo and Stephan Trenn and Francesco Vasca},

url = {https://stephantrenn.net/wp-content/uploads/2022/03/Preprint-MTV220329.pdf, Preprint},

doi = {10.23919/ECC55457.2022.9838189},

year  = {2022},

date = {2022-07-12},

urldate = {2022-07-12},

booktitle = {Proceedings of the 2022 European Control Conference (ECC)},

pages = {1085-1090},

address = {London},

abstract = {Switched descriptor systems with pulse width modulation are characterized by modes whose dynamics are described by differential algebraic equations; this type of models can be viewed as switched impulsive systems, i.e. switched systems with ordinary differential equations as modes dynamics and state jumps at the switching time instants. The presence of possible jumps in the state makes the application of the classical averaging technique nontrivial. In this paper we propose an averaged model for switched impulsive systems. The state trajectory of the proposed averaged model is shown to approximate the one of the original system with an error of order of the switching period. The model reduces to the classical averaged model when there are no jumps in the state. The practical interest of the theoretical averaging result is demonstrated through numerical simulations of a switched capacitor electrical circuit.},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{HuTren22,

title = {Funnel control for relative degree one nonlinear systems with input saturation},

author = {Jiaming Hu and Stephan Trenn and Xiaojin Zhu},

url = {https://stephantrenn.net/wp-content/uploads/2022/03/Preprint-HTZ220329.pdf, Preprint},

doi = {10.23919/ECC55457.2022.9837979},

year  = {2022},

date = {2022-07-12},

urldate = {2022-07-12},

booktitle = {Proceedings of the 2022 European Control Conference (ECC)},

pages = {227-232},

address = {London},

abstract = {The dilemma between transient behavior and accuracy in tracking control arises in both theoretical research and engineering practice and funnel control has shown great potential in solving that problem. Apart from the controlled system, the performance of funnel control strongly depends on the reference signal and the choice of prescribed funnel boundary. In this paper, we will present a new form of funnel controller for systems with control saturation. Compared to former research, the new controller is more reliable, and the closed-loop system can even achieve asymptotic tracking. Besides that, a new concept called constrained funnel boundary is introduced. Together with the new controller and the constrained funnel boundary, the application range of funnel control is extended significantly.},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@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},

doi = {10.1109/CDC45484.2021.9682950},

year  = {2021},

date = {2021-09-27},

urldate = {2021-09-27},

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

pages = {5275-5280},

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.},

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},

doi = {10.1109/CDC45484.2021.9682894},

year  = {2021},

date = {2021-09-07},

urldate = {2021-09-07},

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

pages = {2474-2479},

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.},

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},

doi = {10.23919/ECC54610.2021.9654844},

year  = {2021},

date = {2021-06-29},

urldate = {2021-06-29},

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

pages = {267-292},

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.},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{HossTren21b,

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},

doi = {10.23919/ECC54610.2021.9654948},

year  = {2021},

date = {2021-06-29},

urldate = {2021-06-29},

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

pages = {1168-1173},

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.},

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/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{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/2022/03/ChenTren21c.pdf, Paper

},

doi = {10.1016/j.ifacol.2021.08.496},

year  = {2021},

date = {2021-03-26},

urldate = {2021-03-26},

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

volume = {54},

number = {5},

pages = {187-192},

address = {Brussels, Belgium},

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 = {open access},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}