Publications

@inproceedings{KariTren24,

title = {Funnel control for impulsive switched systems},

author = {Atiyeh Karimi-Pour and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2024/09/Preprint-KT240913.pdf, Preprint},

year  = {2024},

date = {2024-12-16},

urldate = {2024-12-16},

booktitle = {Proc. 63rd IEEE Conf. Decision Control (CDC 2024)},

address = {Milan, Italy},

organization = {IEEE},

abstract = {Impulsive switched systems encompass various modes, each exhibiting distinct behaviours. Typically, a switching sequence orchestrates transitions between these modes, where state jumps may occur, potentially undermining output tracking performance or system stability. This work introduces a funnel controller tailored for relative degree one nonlinear impulsive switched systems. Notably, this controller operates solely based on system output without necessitating knowledge of system dynamics. Unlike classical funnel controllers with fixed boundaries, the proposed method dynamically adjusts the funnel boundary for each approaching jump, aiming to preserve adherence to the original boundary. No precise knowledge of jump instances or maps is required; approximate jump intervals and an upper bound for maximum jump height suffice. Theoretical analysis establishes that the error remains within the funnel, facilitating successful reference signal tracking. Performance validation is demonstrated via numerical simulation.},

note = {to appear},

keywords = {funnel-control, nonlinear, relative-degree, switched-systems},

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{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 = {funnel-control, input-constraints, nonlinear, relative-degree},

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 = {DAEs, nonlinear, solution-theory},

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 = {DAEs, nonlinear, normal-forms, solution-theory},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{ChenTren21a,

title = {The differentiation index of nonlinear differential-algebraic equations versus the relative degree of nonlinear control systems},

author = {Yahao Chen and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2021/01/pamm.202000162.pdf, Paper},

doi = {10.1002/pamm.202000162},

year  = {2021},

date = {2021-01-25},

booktitle = {PAMM · Proc. Appl. Math. Mech. 2020},

volume = {20},

number = {1},

pages = {e202000162},

publisher = {Wiley-VCH GmbH},

abstract = {It is claimed in [1] that the notion of the relative degree in nonlinear control theory is closely related to that of the differen- tiation index for nonlinear differential-algebraic equations (DAEs). In this paper, we give more insights on this claim via a recent proposed concept (see [2]) called the explicitation of DAEs. The explicitation attaches a class of control systems to a given DAE, we show that the relative degree of the systems in the explicitation class is invariant in some sense and that the differentiation index of the original DAE coincides with the maximum of the relative degree of the explicitation systems.},

note = {Open Access.},

keywords = {DAEs, nonlinear, normal-forms, relative-degree},

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

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{KausTren18,

title = {Water hammer modeling for water networks via hyperbolic PDEs and switched DAEs},

author = {Rukhsana Kausar and Stephan Trenn},

editor = {Christian Klingenberg and Michael Westdickenberg},

url = {https://stephantrenn.net/wp-content/uploads/2017/09/Preprint-KT170418.pdf, Preprint},

doi = {10.1007/978-3-319-91548-7_9},

isbn = {978-3-319-91548-7},

year  = {2018},

date = {2018-06-27},

urldate = {2018-06-27},

booktitle = {Theory, Numerics and Applications of Hyperbolic Problems II},

pages = {123-135},

publisher = {Springer},

address = {Cham},

abstract = {In water distribution network instantaneous changes in valve and pump settings introduce jumps and sometimes impulses. In particular, a particular impulsive phenomenon which occurs due to sudden closing of valve is the so called water hammer. It is classically modeled as a system of hyperbolic partial differential equations (PDEs). We observed that under some suitable assumptions the PDEs usually used to describe water flows can be simplified to differential algebraic equations (DAEs). The idea is to model water hammer phenomenon in the switched DAEs framework due to its special feature of studying such impulsive effects. To compare these two modeling techniques, a system of hyperbolic PDE model and the switched DAE model for a simple set up consisting of two reservoirs, six pipes and three valve is presented. The aim of this contribution is to present results of both models as motivation for the claim that a switched DAE modeling framework is suitable for describing a water hammer.},

note = {Presented at XVI International Conference on Hyperbolic Problems (HYP2016), Aachen},

keywords = {application, DAEs, nonlinear, PDEs, piecewise-smooth-distributions, solution-theory, switched-DAEs, switched-systems},

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 = {application, DAEs, nonlinear, piecewise-smooth-distributions, solution-theory, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{Tren17,

title = {Edge-wise funnel synchronization},

author = {Stephan Trenn},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-Tre170523.pdf, Preprint},

doi = {10.1002/pamm.201710378},

issn = {1617-7061},

year  = {2017},

date = {2017-06-01},

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

volume = {17},

number = {1},

pages = {821 - 822},

publisher = {WILEY-VCH Verlag},

abstract = {Recently, it was suggested in [Shim & Trenn 2015] to use the idea of funnel control in the context of synchronization of multi-agent systems. In that approach each agent is able to measure the difference of its own state and the average state of its neighbours and this synchronization error is used in a typical funnel gain feedback law, see e.g. [Ilchmann & Ryan 2008]. Instead of considering one error signal for each node of the coupling graph (corresponding to an agent) it is also possible to consider one error signal for each edge of the graph. In contrast to the node-wise approach this edgewise funnel synchronization approach results (at least in simulations) in a predictable consensus trajectory.},

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

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{KallKaus17,

title = {Modeling water hammers via PDEs and switched DAEs with numerical justification},

author = {Jochen Kall and Rukhsana Kausar and Stephan Trenn},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-KKT170324.pdf, Preprint},

doi = {10.1016/j.ifacol.2017.08.927},

issn = {2405-8963},

year  = {2017},

date = {2017-03-23},

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

journal = {IFAC-PapersOnLine},

volume = {50},

number = {1},

pages = {5349 - 5354},

address = {Toulouse, France},

abstract = {In water distribution networks instantaneous changes in valve and pump settings may introduces jumps and peaks in the pressure. In particular, a well known phenomenon in response to the sudden closing of a valve is the so called water hammer, which (if not taken into account properly) may destroy parts of the water network. It is classically modeled as a system of hyperbolic partial differential equations (PDEs). After discussing this PDE model we propose a simplified model using switched differential-algebraic equations (DAEs). Switched DAEs are known to be able to produce infinite peaks in response to sudden structural changes. These peaks (in the mathematical form of Dirac impulses) can easily be predicted and may allow for a simpler analysis of complex water networks in the future. As a first step toward that goal, we verify the novel modeling approach by comparing these two modeling techniques numerically for a simple set up consisting of two reservoirs, a pipe and a valve.},

keywords = {application, DAEs, nonlinear, PDEs, solution-theory, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{CamlIann16,

title = {Differential-algebraic inclusions with maximal monotone operators},

author = {Kanat Camlibel and Luigi Iannelli and Aneel Tanwani and Stephan Trenn},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-CITT160923.pdf, Preprint},

doi = {10.1109/CDC.2016.7798336},

year  = {2016},

date = {2016-12-01},

booktitle = {Proc. 55th IEEE Conf. Decis. Control, Las Vegas, USA},

pages = {610--615},

abstract = {The term differential-algebraic inclusions (DAIs) not only describes the dynamical relations using set-valued mappings, but also includes the static algebraic inclusions, and this paper considers the problem of existence of solutions for a class of such dynamical systems described by the inclusion ddt Px in -M(x) for a symmetric positive semi-definite matrix P in R^(n x n), and a maximal monotone operator M:R^n => R^n. The existence of solutions is proved using the tools from the theory of maximal monotone operators. The class of solutions that we study in the paper have the property that, instead of the whole state, only Px is absolutely continuous and unique. This framework, in particular, is useful for studying passive differential-algebraic equations (DAEs) coupled with maximal monotone relations. Certain class of irregular DAEs are also covered within the proposed general framework. Applications from electrical circuits are included to provide a practical motivation.},

keywords = {DAEs, nonlinear, solution-theory},

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{GrosTren14,

title = {Topological solvability and index characterizations for a common DAE power system model},

author = {Tjorben B. Gross and Stephan Trenn and Andreas Wirsen},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-GTW140904.pdf, Preprint},

doi = {10.1109/CCA.2014.6981321},

year  = {2014},

date = {2014-10-10},

booktitle = {Proc. 2014 IEEE Conf. Control Applications (CCA)},

pages = {9--14},

organization = {IEEE},

abstract = {For the widely-used power system model consisting of the generator swing equations and the power flow equations resulting in a system of differential algebraic equations (DAEs), we introduce a sufficient and necessary solvability condition for the linearized model. This condition is based on the topological structure of the power system. Furthermore we show sufficient conditions for the linearized DAE-system and a nonlinear version of the model to have differentiation index equal to one.},

keywords = {application, DAEs, networks, nonlinear, solution-theory},

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{LibeTren13a,

title = {The bang-bang funnel controller: time delays and case study},

author = {Daniel Liberzon and Stephan Trenn},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-LT130320.pdf, Preprint

http://ieeexplore.ieee.org/document/6669120, IEEE Xplore Article Number 6669120},

year  = {2013},

date = {2013-07-01},

booktitle = {Proc. 12th European Control Conf. (ECC) 2013, Zurich, Switzerland},

pages = {1669--1674},

abstract = {We investigate the recently introduced bang-bang funnel controller with respect to its robustness to time delays. We present slightly modified feasibility conditions and prove that the bang-bang funnel controller applied to a relative-degree-two nonlinear system can tolerate sufficiently small time delays. A second contribution of this paper is an extensive case study, based on a model of a real experimental setup, where implementation issues such as the necessary sampling time and the conservativeness of the feasibility assumptions are explicitly considered.},

keywords = {application, funnel-control, input-constraints, nonlinear, relative-degree},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{HackTren12,

title = {The bang-bang funnel controller: An experimental  verification},

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

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-HT120427.pdf, Preprint},

doi = {10.1002/pamm.201210356},

year  = {2012},

date = {2012-03-01},

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

volume = {12},

number = {1},

pages = {735--736},

publisher = {Wiley-VCH Verlag GmbH},

address = {Weinheim},

organization = {GAMM Annual Meeting 2012, Darmstadt},

abstract = {We adjust the newly developed bang-bang funnel controller such that it is more applicable for real world scenarios. The main idea is to introduce a third “neutral” input value to account for the situation when the error is already small enough and no control action is necessary. We present experimental results to illustrate the effectiveness of our new approach in the case of position control of an electrical drive.},

keywords = {application, funnel-control, input-constraints, nonlinear, relative-degree},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{LibeTren10,

title = {The bang-bang funnel controller},

author = {Daniel Liberzon and Stephan Trenn},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-LT100806.pdf, Preprint

http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-LT100806longVersion.pdf, Preprint (long version)},

doi = {10.1109/CDC.2010.5717742},

year  = {2010},

date = {2010-12-15},

booktitle = {Proc. 49th IEEE Conf. Decis. Control, Atlanta, USA},

pages = {690--695},

abstract = {A bang-bang controller is proposed which is able to ensure reference signal tracking with prespecified time-varying error bounds (the funnel) for nonlinear systems with relative degree one or two. For the design of the controller only the knowledge of the relative degree is needed. The controller is guaranteed to work when certain feasibility assumptions are fulfilled, which are explicitly given in the main results. Linear systems with relative degree one or two are feasible if the system is minimum phase and the control values are large enough.},

keywords = {funnel-control, input-constraints, nonlinear, relative-degree},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{MandTren06,

title = {Analogue Implementation of the funnel controller},

author = {Nagendra P. Mandaloju and Stephan Trenn},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-MT060428.pdf, Preprint},

doi = {10.1002/pamm.200610391},

issn = {1617-7061},

year  = {2006},

date = {2006-05-01},

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

volume = {6},

number = {1},

pages = {823--824},

publisher = {WILEY-VCH Verlag},

abstract = {In many tracking control problems, pre-specified bounds for the evolution of the tracking error should be met. The ‘funnel controller’ addresses this requirement and guarantees transient performance for a fairly large class of systems. In addition, only structural assumptions on the underlying system are made; the exact knowledge of the system parameters is not required. This is in contrast to most classical controllers where only asymptotic behaviour can be guaranteed and the system parameters must be known or estimated. Until now, the funnel controller was only studied theoretically. We will present the results of an analogue implementation of the funnel controller. The results show that the funnel controller works well in reality, i.e. it guarantees the pre-specified error bounds. The implementation is an analogue circuit composed of standard devices and is therefore suitable for a broad range of applications.},

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

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}

}