Publications

@article{LanzDann24,

title = {Sampled-data funnel control and its use for safe continual learning},

author = {Lukas Lanza and Dario Dennstädt and Karl Worthmann and Philipp Schmitz and Gökcen Devlet Sen and Stephan Trenn and Manuel Schaller},

url = {https://stephantrenn.net/wp-content/uploads/2024/09/LanzDenn24.pdf, Paper

https://arxiv.org/abs/2303.00523, arXiv},

doi = {10.1016/j.sysconle.2024.105892},

year  = {2024},

date = {2024-08-09},

urldate = {2024-08-09},

journal = {Systems & Control Letters},

volume = {192},

number = {105892},

pages = {1-12},

abstract = {We propose a novel sampled-data output-feedback controller for nonlinear systems of arbitrary relative degree that ensures reference tracking within prescribed error bounds. We provide explicit bounds on the maximum input signal and the required uniform sampling time. A key strength of this approach is its capability to serve as a safety filter for various learning-based controller designs, enabling the use of learning techniques in safety- critical applications. We illustrate its versatility by integrating it with two different controllers: a reinforcement learning controller and a non-parametric predictive controller based on Willems et al.’s fundamental lemma. Numerical simulations illustrate effectiveness of the combined controller design.},

note = {open access},

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

pubstate = {published},

tppubtype = {article}

}

@article{HuTren23,

title = {A novel two stages funnel controller limiting the error derivative},

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

url = {https://stephantrenn.net/wp-content/uploads/2024/02/HuTren23.pdf, Paper},

doi = {10.1016/j.sysconle.2023.105601},

year  = {2023},

date = {2023-09-01},

urldate = {2023-09-01},

journal = {Systems & Control Letters},

volume = {179},

number = {105601},

pages = {1-10},

abstract = {As a powerful adaptive control method for the output tracking problem, funnel control has attracted considerable attention in theoretical research and engineering practice. The funnel control strategy can guarantee both transient behavior and arbitrary good accuracy. A noticeable shortcoming is however that the derivative of the tracking error may become unnecessarily large resulting in a bouncing behavior of the tracking error between the funnel boundaries. To avoid this phenomenon, we present a novel two stages funnel control scheme to solve the output-tracking control problem for uncertain nonlinear systems with relative degree one and stable internal dynamics. This new scheme defines the control input in terms of a desired error derivative while still ensuring that the tracking error evolves within the prescribed funnel. In particular, we can quantify the range of the error derivative with a derivative funnel in terms of the known bounds of the system dynamics. Furthermore, we extend our approach to the situation where input saturations are present and extend the control law outside the funnel to ensure well-defined behavior in case the input saturations are too restrictive to keep the error within the funnel.},

note = {open access},

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

pubstate = {published},

tppubtype = {article}

}

@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{IlchSawo06,

title = {Pneumatic cylinders: modelling and feedback force-control},

author = {Achim Ilchmann and Oliver Sawodny and Stephan Trenn},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-IST050502.pdf, Preprint},

doi = {10.1080/00207170600645875},

year  = {2006},

date = {2006-01-01},

journal = {Int. J. Control},

volume = {79},

number = {6},

pages = {650--661},

abstract = {In this paper, we model, analyse, and control an experimental set-up of a servo pneumatic cylinder. The dynamic behaviour of pneumatic actuator systems is dominant by non-linear functions. First, a mathematical model for the pneumatic system is derived. Secondly, we investigate the mathematical properties of this model and show boundedness and positiveness of certain variables. Thirdly, we prove that a proportional output feedback controller with saturation achieves practical tracking a wide class of reference trajectories. We verify the theoretical results and the effectiveness of the control by experiments.},

keywords = {application, input-constraints},

pubstate = {published},

tppubtype = {article}

}

@article{IlchTren04,

title = {Input constrained funnel control with applications to  chemical reactor models},

author = {Achim Ilchmann and Stephan Trenn},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-IT040715.pdf, Preprint},

doi = {10.1016/j.sysconle.2004.05.014},

year  = {2004},

date = {2004-01-01},

journal = {Syst. Control Lett.},

volume = {53},

number = {5},

pages = {361--375},

publisher = {Elsevier},

abstract = {Error feedback control is considered for a class of exothermic chemical reactor models. The control objective is that the temperature T evolves within a prespecified performance envelope or ``funnel'' around the set point temperature T*. A simple error feedback control with input constraints of the form u(t)=sat(-k(t)[T(t)-T*] + u*), u* an offset, is introduced which achieves the objective in the presence of disturbances corrupting the measurement. The gain k(t) is a function of the error e(t)=T(t)-T* and its distance to the funnel boundary. The input constraints have to satisfy certain feasibility assumptions in terms of the model data and the operating point T*.},

keywords = {application, funnel-control, input-constraints},

pubstate = {published},

tppubtype = {article}

}