Publications

@article{LibeTren13b,
title = {The bang-bang funnel controller for uncertain nonlinear systems with arbitrary relative degree},
author = {Daniel Liberzon and Stephan Trenn},
url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-LT130702.pdf, Preprint},
doi = {10.1109/TAC.2013.2277631},
year = {2013},
date = {2013-08-16},
journal = {IEEE Trans. Autom. Control},
volume = {58},
number = {12},
pages = {3126--3141},
abstract = {The paper considers output tracking control of uncertain nonlinear systems with arbitrary known relative degree and known sign of the high frequency gain. The tracking objective is formulated in terms of a time-varying bound-a funnel-around a given reference signal. The proposed controller is bang-bang with two control values. The controller switching logic handles arbitrarily high relative degree in an inductive manner with the help of auxiliary derivative funnels. We formulate a set of feasibility assumptions under which the controller maintains the tracking error within the funnel. Furthermore, we prove that under mild additional assumptions the considered system class satisfies these feasibility assumptions if the selected control values are sufficiently large in magnitude. Finally, we study the effect of time delays in the feedback loop and we are able to show that also in this case the proposed bang-bang funnel controller works under slightly adjusted feasibility assumptions.},
keywords = {funnel-control, input-constraints, nonlinear, relative-degree},
pubstate = {published},
tppubtype = {article}
}

@article{HackHopf13,
title = {Funnel control for systems with relative degree two},
author = {Christoph M. Hackl and Norman Hopfe and Achim Ilchmann and Markus Mueller and Stephan Trenn},
url = {http://stephantrenn.net/wp-content/uploads/2017/09/HackHopf13.pdf, Paper},
doi = {10.1137/100799903 },
year = {2013},
date = {2013-03-19},
journal = {SIAM J. Control Optim.},
volume = {51},
number = {2},
pages = {965--995},
abstract = {Tracking of reference signals y_ref(.) by the output y(.) of linear (as well as a considerably large class of nonlinear) single-input, single-output systems is considered. The system is assumed to have strict relative degree two with (weakly) stable zero dynamics. The control objective is tracking of the error e=y-y_ref and its derivative e' within two prespecified performance funnels, respectively. This is achieved by the so-called funnel controller u(t) = -k_0(t)^2 e(t) - k_1(t) e'(t), where the simple proportional error feedback has gain functions k_0 and k_1 designed in such a way to preclude contact of e and e' with the funnel boundaries, respectively. The funnel controller also ensures boundedness of all signals. We also show that the same funnel controller (i) is applicable to relative degree one systems, (ii) allows for input constraints provided a feasibility condition (formulated in terms of the system data, the saturation bounds, the funnel data, bounds on the reference signal, and the initial state) holds, (iii) is robust in terms of the gap metric: if a system is sufficiently close to a system with relative degree two, stable zero dynamics, and positive high-frequency gain, but does not necessarily have these properties, then for small initial values the funnel controller also achieves the control objective. Finally, we illustrate the theoretical results by experimental results: the funnel controller is applied to a rotatory mechanical system for position control.},
keywords = {application, funnel-control, input-constraints, nonlinear, relative-degree},
pubstate = {published},
tppubtype = {article}
}

@article{Tren09a,
title = {A normal form for pure differential algebraic systems},
author = {Stephan Trenn},
url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-Tre081215.pdf, Preprint},
doi = {10.1016/j.laa.2008.10.004},
year = {2009},
date = {2009-01-01},
journal = {Linear Algebra Appl.},
volume = {430},
number = {4},
pages = {1070 -- 1084},
abstract = {In this paper linear time-invariant differential algebraic equations (DAEs) are studied; the focus is on pure DAEs which are DAEs without an ordinary differential equation (ODE) part. A normal form for pure DAEs is given which is similar to the Byrnes–Isidori normal form for ODEs. Furthermore, the normal form exhibits a Kalman-like decomposition into impulse-controllable- and impulse-observable states. This leads to a characterization of impulse-controllability and observability.},
keywords = {controllability, DAEs, normal-forms, observability, relative-degree},
pubstate = {published},
tppubtype = {article}
}