Publications

@inproceedings{BergHack24,

title = {Asymptotic tracking by funnel control with internal models},

author = {Thomas Berger and Christoph M. Hackl and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2024/03/Preprint-BHT240326.pdf, Preprint

https://arxiv.org/abs/2310.15544, arXiv},

doi = {10.23919/ECC64448.2024.10590783},

year  = {2024},

date = {2024-06-25},

urldate = {2024-06-25},

booktitle = {Proc. European Control Conference (ECC24)},

pages = {1776-1781},

publisher = {IEEE},

address = {Stockholm, Sweden},

abstract = {Funnel control achieves output tracking with guaranteed tracking performance for unknown systems and arbitrary reference signals. In particular, the tracking error is guaranteed to satisfy time-varying error bounds for all times (it evolves in the funnel). However, convergence to zero cannot be guaranteed, but the error often stays close to the funnel boundary, inducing a comparatively large feedback gain. This has several disadvantages (e.g. poor tracking performance and sensitivity to noise due to the underlying high-gain feedback principle). In this paper, therefore, the usually known reference signal is taken into account during funnel controller design, i.e. we propose to combine the well-known internal model principle with funnel control. We focus on linear systems with linear reference internal models and show that under mild adjustments of funnel control, we can achieve asymptotic tracking for a whole class of linear systems (i.e. without relying on the knowledge of system parameters).},

keywords = {funnel-control, relative-degree, stability},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{ChanTren23,

title = {Design of Q-filter-based disturbance observer for differential algebraic equations and a robust stability condition: Zero relative degree case},

author = {Hamin Chang and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2023/11/Preprint-CT230915.pdf, Preprint},

doi = {10.1109/CDC49753.2023.10383698},

year  = {2023},

date = {2023-12-15},

urldate = {2023-12-15},

booktitle = {Proc. 62nd IEEE Conf. Decision Control},

pages = {8489-8494},

publisher = {IEEE},

abstract = {While the disturbance observer (DOB)-based controller is widely utilized in various practical applications, there has been a lack of extension of its use to differential algebraic equations (DAEs). In this paper, we introduce several lemmas that establish necessary and/or sufficient conditions for specifying the relative degree of DAEs. Using these lemmas, we also figure out that there is a class of DAEs which can be viewed as linear systems with zero relative degree. For the class of DAEs, we propose a design of Q-filter-based DOB as well as a robust stability condition for systems controlled by the DOB through time domain analysis using singular perturbation theory. The proposed stability condition is verified by an illustrative example.},

keywords = {DAEs, observer, relative-degree, stability},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{SutrYin23,

title = {Nonlinear singular switched systems in discrete-time: solution theory and incremental stability under restricted switching signals},

author = {Sutrisno and Hao Yin and Stephan Trenn and Bayu Jayawardhana},

url = {https://stephantrenn.net/wp-content/uploads/2023/11/Preprint-SYTJ230914.pdf, Preprint},

doi = {10.1109/CDC49753.2023.10383278},

year  = {2023},

date = {2023-12-13},

urldate = {2023-09-14},

booktitle = {Proc. 62nd IEEE Conf. Decision Control},

pages = {914-919},

publisher = {IEEE},

address = {Singapore},

abstract = {In this article the solvability analysis of discrete-time nonlinear singular switched systems with restricted switching signals is studied. We provide necessary and sufficient conditions for the solvability analysis under fixed switching signals and fixed mode sequences. The so-called surrogate systems (ordinary systems that have the equivalent behavior to the original switched systems) are introduced for solvable switched systems. Incremental stability, which ensures that all solution trajectories converge with each other, is then studied by utilizing these surrogate systems. Sufficient (and necessary) conditions are provided for this stability analysis using single and switched Lyapunov function approaches.},

keywords = {DAEs, discrete-time, nonlinear, solution-theory, stability, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@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 = {DAEs, nonlinear, solution-theory, stability, switched-DAEs, switched-systems},

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 = {DAEs, stability, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{Tren19,

title = {Asymptotic tracking with funnel control},

author = {Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2019/11/45-PAMM19-201900071.pdf, Paper},

doi = {10.1002/pamm.201900071},

year  = {2019},

date = {2019-09-09},

booktitle = {PAMM - Proc. Appl. Math. Mech.},

journal = {PAMM - Proc. Appl. Math. Mech.},

publisher = {WILEY-VCH Verlag},

abstract = {Funnel control is a strikingly simple control technique to ensure model free practical tracking for quite general nonlinear systems. It has its origin in the adaptive control theory, in particular, it is based on the principle of high gain feedback control. The key idea of funnel control is to chose the feedback gain large when the tracking error approaches the prespecified error tolerance (the funnel boundary). It was long believed that it is a theoretical limitation of funnel control not being able to achieve asymptotic tracking, however, in this contribution it will be shown that this is not the case.},

note = {online},

keywords = {funnel-control, stability},

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 = {application, stability, switched-DAEs, switched-systems},

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},

urldate = {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 piecewise 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 = {LMIs, stability, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{TanwTren17b,

title = {Observer design for detectable switched  differential-algebraic equations},

author = {Aneel Tanwani and Stephan Trenn},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-TT170320.pdf, Preprint},

doi = {10.1016/j.ifacol.2017.08.659},

issn = {2405-8963},

year  = {2017},

date = {2017-03-22},

booktitle = {Proc. 20th IFAC World Congress 2017},

journal = {IFAC-PapersOnLine},

volume = {50},

number = {1},

pages = {2953 - 2958},

address = {Toulouse, France},

abstract = {This paper studies detectability for switched linear differential-algebraic equations (DAEs) and its application in synthesis of observers. Equating detectability to asymptotic stability of zero-output-constrained state trajectories, and building on our work on interval-wise observability, we propose the notion of interval-wise detectability: If the output of the system is constrained to be identically zero over an interval, then the norm of the corresponding state trajectories scales down by a certain factor over that interval. Conditions are provided under which the interval-wise detectability leads to asymptotic stability of zero-output-constrained state trajectories. An application is demonstrated in designing state estimators. Decomposing the state into observable and unobservable components, we show that if the observable component in the estimator is reset appropriately and persistently, then the estimation error converges to zero asymptotically under the interval-wise detectability assumption.},

keywords = {DAEs, observability, observer, piecewise-smooth-distributions, stability, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{Tren16,

title = {Stabilization of switched DAEs via fast switching},

author = {Stephan Trenn},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-Tre160511.pdf, Preprint},

doi = {10.1002/pamm.201610402},

issn = {1617-7061},

year  = {2016},

date = {2016-05-12},

booktitle = {PAMM - Proc. Appl. Math. Mech.},

volume = {16},

number = {1},

pages = {827--828},

publisher = {WILEY-VCH Verlag},

abstract = {Switched differential algebraic equations (switched DAEs) can model dynamical systems with state constraints together with sudden structural changes (switches). These switches may lead to induced jumps and can destabilize the system even in the case that each mode is stable. However, the opposite effect is also possible; in particular, the question of finding a stabilizing switching signal is of interest. Two approaches are presented how to stabilize a switched DAE via fast switching.},

keywords = {averaging, DAEs, stability, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{TanwTren15,

title = {On detectability of switched linear differential-algebraic  equations},

author = {Aneel Tanwani and Stephan Trenn},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-TT150904.pdf, Preprint},

doi = {10.1109/CDC.2015.7402666},

year  = {2015},

date = {2015-12-03},

booktitle = {Proc. 54th IEEE Conf. Decis. Control, Osaka, Japan},

pages = {2957--2962},

abstract = {This paper addresses the notion of detectability for continuous-time switched systems comprising linear differential-algebraic equations (DAEs). It relates to studying asymptotic stability of the set of state trajectories corresponding to zero input and zero output, with a fixed switching signal. Due to the nature of solutions of switched DAEs, the problem reduces to analyzing stability of the trajectories emanating from a non-vanishing unobservable subspace, for which we first derive a geometric expression. The stability of state trajectories starting from that subspace can then be checked in two possible ways. In the first case, detectability of switched DAE is shown to be equivalent to the asymptotic stability of a reduced order discrete-time switched system. In the second approach, the solutions from a non-vanishing unobservable subspace are mapped to the solutions of a reduced order continuous system with time-varying switching ordinary differential equations (ODEs). As a special case of the later approach, the reduced order switched system is time-invariant if the unobservable subspace is invariant for all subsystems},

keywords = {DAEs, observability, stability, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{ShimTren15,

title = {A preliminary result on synchronization of heterogeneous agents via funnel control},

author = {Hyungbo Shim and Stephan Trenn},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-ST150902.pdf, Preprint},

doi = {10.1109/CDC.2015.7402538},

year  = {2015},

date = {2015-12-01},

booktitle = {Proc. 54th IEEE Conf. Decis. Control, Osaka, Japan},

pages = {2229--2234},

abstract = {We propose a new approach to achieve practical synchronization for heterogeneous agents. Our approach is based on the observation that a sufficiently large (but constant) gain for diffusive coupling leads to practical synchronization. In the classical setup of high-gain adaptive control, the funnel controller gained popularity in the last decade, because it is very simple and only structural knowledge of the underlying dynamical system is needed. We illustrate with simulations that “funnel synchronization” may be a promising approach to achieve practical synchronization of heterogeneous agents without the need to know the individual dynamics and the algebraic connectivity of the network (i.e., the second smallest eigenvalue of the Laplacian matrix). For a special case we provide a proof, but the proof for the general case is ongoing research.},

keywords = {funnel-control, networks, nonlinear, stability, synchronization},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{DefoDjem14,

title = {Nondecreasing Lyapunov functions},

author = {Michael Defoort and Mohamed Djemai and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2024/01/DefoDjem14.pdf, Paper

http://fwn06.housing.rug.nl/mtns/?page_id=38, Proceedings Website},

year  = {2014},

date = {2014-07-01},

urldate = {2014-07-01},

booktitle = {Proc. 21st Int. Symposium Math. Theory Networks Systems (MTNS)},

pages = {1038--1043},

abstract = {We propose the notion of nondecreasing Lyapunov functions which can be used to prove stability or other properties of the system in question. This notion is in particular useful in studying switched or hybrid systems. We illustrate the concept by a general construction of such a nondecreasing Lyapunov function for a class of planar hybrid systems. It is noted that this class encompasses switched systems for which no piecewise-quadratic (classical) Lyapunov function exists.},

keywords = {Lyapunov, nonlinear, stability, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{TrenWirt12b,

title = {Linear switched DAEs: Lyapunov exponents, a converse Lyapunov theorem, and Barabanov norms},

author = {Stephan Trenn and Fabian Wirth},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-TW120901.pdf, Preprint},

doi = {10.1109/CDC.2012.6426245},

issn = {0191-2216},

year  = {2012},

date = {2012-12-12},

booktitle = {Proc. 51st IEEE Conf. Decis. Control, Maui, USA},

pages = {2666--2671},

abstract = {For linear switched differential algebraic equations (DAEs) we consider the problem of characterizing the maximal exponential growth rate of solutions. It is shown that a finite exponential growth rate exists if and only if the set of consistency projectors associated to the family of DAEs is product bounded. This result may be used to derive a converse Lyapunov theorem for switched DAEs. Under the assumption of irreducibility we show that a construction reminiscent of the construction of Barabanov norms is feasible as well.},

keywords = {DAEs, Lyapunov, stability, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{TrenWirt12a,

title = {A converse Lyapunov theorem for switched DAEs},

author = {Stephan Trenn and Fabian Wirth},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-TW120508.pdf, Preprint},

doi = {10.1002/pamm.201210381},

issn = {1617-7061},

year  = {2012},

date = {2012-03-02},

booktitle = {PAMM - Proc. Appl. Math. Mech.},

volume = {12},

number = {1},

pages = {789--792},

publisher = {WILEY-VCH Verlag},

abstract = {For switched ordinary differential equations (ODEs) it is well known that exponential stability under arbitrary switching yields the existence of a common Lyapunov function. The result is known as a “converse Lyapunov Theorem”. In this note we will present a converse Lyapunov theorem for switched differential algebraic equations (DAEs) as well as the construction of a Barabanov norm for irreducible switched DAEs.},

keywords = {DAEs, Lyapunov, stability, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{LibeTren11,

title = {Commutativity and asymptotic stability for linear switched  DAEs},

author = {Daniel Liberzon and Stephan Trenn and Fabian Wirth},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-LTW110816.pdf, Preprint},

doi = {10.1109/CDC.2011.6160335},

year  = {2011},

date = {2011-12-01},

booktitle = {Proc. 50th IEEE Conf. Decis. Control and European Control Conf. ECC 2011, Orlando, USA},

pages = {417--422},

abstract = {For linear switched ordinary differential equations with asymptotically stable constituent systems, it is well known that commutativity of the coefficient matrices implies asymptotic stability of the switched system under arbitrary switching. This result is generalized to linear switched differential algebraic equations (DAEs). Although the solutions of a switched DAE can exhibit jumps it turns out that it suffices to check commutativity of the “flow” matrices. As in the ODE case we are also able to construct a common quadratic Lyapunov function.},

keywords = {DAEs, Lyapunov, stability, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{LibeTren09,

title = {On stability of linear switched differential algebraic equations},

author = {Daniel Liberzon and Stephan Trenn},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-LT090903.pdf, Preprint},

doi = {10.1109/CDC.2009.5400076},

year  = {2009},

date = {2009-12-01},

booktitle = {Proc. Joint 48th IEEE Conf. Decis. Control and 28th Chinese Control Conf.},

pages = {2156--2161},

abstract = {This paper studies linear switched differential algebraic equations (DAEs), i.e., systems defined by a finite family of linear DAE subsystems and a switching signal that governs the switching between them. We show by examples that switching between stable subsystems may lead to instability, and that the presence of algebraic constraints leads to a larger variety of possible instability mechanisms compared to those observed in switched systems described by ordinary differential equations (ODEs). We prove two sufficient conditions for stability of switched DAEs based on the existence of suitable Lyapunov functions. The first result states that a common Lyapunov function guarantees stability under arbitrary switching when an additional condition involving consistency projectors holds (this extra condition is not needed when there are no jumps, as in the case of switched ODEs). The second result shows that stability is preserved under switching with sufficiently large dwell time.},

keywords = {DAEs, Lyapunov, stability, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{FrenTren05,

title = {l^{p} gain bounds for switched adaptive controllers},

author = {Mark French and Stephan Trenn},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-FT050913.pdf, Preprint},

doi = {10.1109/CDC.2005.1582598},

year  = {2005},

date = {2005-12-01},

booktitle = {Proc. 44th IEEE Conf. Decis. Control and European Control Conf. (ECC)},

pages = {2865--2870},

abstract = {A class of discrete plants controlled by a switching adaptive strategy is considered, and l^p bounds, 1 ≤ p ≤ ∞, are obtained for the closed loop gain relating input and output disturbances to internal signals.},

keywords = {stability, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{IlchRyan04b,

title = {Adaptive tracking within prescribed funnels},

author = {Achim Ilchmann and Eugene P. Ryan and Stephan Trenn},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-IRT040512.pdf, Preprint},

doi = {10.1109/CCA.2004.1387507},

year  = {2004},

date = {2004-09-01},

booktitle = {Proc. 2004 IEEE Int. Conf. Control Appl.},

volume = {2},

pages = {1032--1036},

abstract = {Output tracking of a reference signal (an absolutely continuous bounded function with essentially bounded derivative) is considered in a context of a class of nonlinear systems described by functional differential equations. The primary control objective is tracking with prescribed accuracy: given lambda > 0 (arbitrarily small), ensure that, for every admissible system and reference signal, the tracking error e is ultimately smaller than lambda (that is, ||e(t)|| < lambda for all t sufficiently large). The second objective is guaranteed transient performance: the evolution of the tracking error should be contained in a prescribed performance funnel F. Adopting the simple feedback control structure u(t) = -k(t)e(t), it is shown that the above objectives can be achieved if the gain k(t) = K_F(t,e(t)) is generated by any continuous function K_F exhibiting two specific properties formulated in terms of the distance of e(t) to the funnel boundary.},

keywords = {funnel-control, nonlinear, stability},

pubstate = {published},

tppubtype = {inproceedings}

}