2022
|
Hossain, Sumon; Sutrisno,; Trenn, Stephan A time-varying approach for model reduction of singular linear switched systems in discrete time Miscellaneous Extended Abstracts of the 25th International Symposium on Mathematical Theory of Networks and Systems, 2022. @misc{HossSutr22m,
title = {A time-varying approach for model reduction of singular linear switched systems in discrete time},
author = {Sumon Hossain and Sutrisno and Stephan Trenn},
url = {https://epub.uni-bayreuth.de/id/eprint/6809/, Book of Extended Abstracts
https://stephantrenn.net/wp-content/uploads/2023/01/HossSutr22m.pdf, Extended Abtract},
year = {2022},
date = {2022-09-12},
urldate = {2023-01-23},
abstract = {We propose a model reduction approach for singular linear switched systems in discrete time with a fixed mode sequence based on a balanced truncation reduction method for linear time-varying discrete-time systems. The key idea is to use the one-step map to find an equivalent time-varying system with an identical input-output behavior, and then adapt available balance truncation methods for (discrete) time-varying systems. The proposed method is illustrated with a low-dimensional academic example.},
howpublished = {Extended Abstracts of the 25th International Symposium on Mathematical Theory of Networks and Systems},
keywords = {controllability, DAEs, discrete-time, model-reduction, observability, switched-DAEs, switched-systems},
pubstate = {published},
tppubtype = {misc}
}
We propose a model reduction approach for singular linear switched systems in discrete time with a fixed mode sequence based on a balanced truncation reduction method for linear time-varying discrete-time systems. The key idea is to use the one-step map to find an equivalent time-varying system with an identical input-output behavior, and then adapt available balance truncation methods for (discrete) time-varying systems. The proposed method is illustrated with a low-dimensional academic example. |
Wijnbergen, Paul; Trenn, Stephan Linear quadratic optimal control of switched differential algebraic equations Miscellaneous Extended Abstracts of the 25th International Symposium on Mathematical Theory of Networks and Systems, 2022. @misc{WijnTren22mb,
title = {Linear quadratic optimal control of switched differential algebraic equations},
author = {Paul Wijnbergen and Stephan Trenn},
url = {https://epub.uni-bayreuth.de/id/eprint/6809/, Book of Extended Abstracts
https://stephantrenn.net/wp-content/uploads/2023/01/WijnTren22mb.pdf, Extended Abstract},
year = {2022},
date = {2022-09-12},
urldate = {2022-09-12},
abstract = {In this abstract the finite horizon linear quadratic optimal control problem with constraints on the terminal state for switched differential algebraic equations is considered. Furthermore, we seek for an optimal solution that is impulse-free. In order to solve the problem, a non standard finite horizon problem for non-switched DAEs is considered. Necessary and sufficient conditions on the initial value x0 for solvability of this non standard problem are stated. Based on these results a sequence of subspaces can be defined which lead to necessary and sufficient conditions for solvability of the finite horizon optimal control problem for switched DAEs.},
howpublished = {Extended Abstracts of the 25th International Symposium on Mathematical Theory of Networks and Systems},
keywords = {DAEs, optimal-control, switched-DAEs, switched-systems},
pubstate = {published},
tppubtype = {misc}
}
In this abstract the finite horizon linear quadratic optimal control problem with constraints on the terminal state for switched differential algebraic equations is considered. Furthermore, we seek for an optimal solution that is impulse-free. In order to solve the problem, a non standard finite horizon problem for non-switched DAEs is considered. Necessary and sufficient conditions on the initial value x0 for solvability of this non standard problem are stated. Based on these results a sequence of subspaces can be defined which lead to necessary and sufficient conditions for solvability of the finite horizon optimal control problem for switched DAEs. |
Sutrisno,; Trenn, Stephan The one-step function for discrete-time nonlinear switched singular systems Miscellaneous Book of Abstracts - 41th Benelux Meeting on Systems and Control, 2022. @misc{SutrTren22m,
title = {The one-step function for discrete-time nonlinear switched singular systems},
author = {Sutrisno and Stephan Trenn},
editor = {Alain Vande Wouwer and Michel Kinnaert and Emanuele Garone and Laurent Dewasme and Guilherme A. Pimentel},
url = {https://stephantrenn.net/wp-content/uploads/2022/08/SutrTren22.pdf, Abstract
https://www.beneluxmeeting.nl/2022/uploads/images/2022/boa_BeneluxMeeting2022_Web_betaV12_withChairs.pdf, Book of Abstracts},
year = {2022},
date = {2022-07-07},
urldate = {2022-07-07},
howpublished = {Book of Abstracts - 41th Benelux Meeting on Systems and Control},
keywords = {discrete-time, nonlinear, solution-theory, switched-DAEs, switched-systems},
pubstate = {published},
tppubtype = {misc}
}
|
Yin, Hao; Jayawardhana, Bayu; Trenn, Stephan On contraction analysis of switched systems with mixed contracting-noncontracting modes via mode-dependent average dwell time Miscellaneous Book of Abstracts - 41th Benelux Meeting on Systems and Control, 2022. @misc{YinJaya22m,
title = {On contraction analysis of switched systems with mixed contracting-noncontracting modes via mode-dependent average dwell time},
author = {Hao Yin and Bayu Jayawardhana and Stephan Trenn},
editor = {Alain Vande Wouwer and Michel Kinnaert and Emanuele Garone and Laurent Dewasme and Guilherme A. Pimentel},
url = {https://stephantrenn.net/wp-content/uploads/2022/08/YinJaya22.pdf, Abstract
https://www.beneluxmeeting.nl/2022/uploads/images/2022/boa_BeneluxMeeting2022_Web_betaV12_withChairs.pdf, Book of Abstracts},
year = {2022},
date = {2022-07-07},
urldate = {2022-07-07},
howpublished = {Book of Abstracts - 41th Benelux Meeting on Systems and Control},
keywords = {LMIs, Lyapunov, stability, switched-systems, synchronization},
pubstate = {published},
tppubtype = {misc}
}
|
Wijnbergen, Paul; Trenn, Stephan Impulse-controllability of system classes of switched DAEs Miscellaneous Book of Abstracts - 41th Benelux Meeting on Systems and Control, 2022. @misc{WijnTren22ma,
title = {Impulse-controllability of system classes of switched DAEs},
author = {Paul Wijnbergen and Stephan Trenn},
editor = {Alain Vande Wouwer and Michel Kinnaert and Emanuele Garone and Laurent Dewasme and Guilherme A. Pimentel},
url = {https://stephantrenn.net/wp-content/uploads/2022/08/WijnTren22ma.pdf, Abstract
https://www.beneluxmeeting.nl/2022/uploads/images/2022/boa_BeneluxMeeting2022_Web_betaV12_withChairs.pdf, Book of Abstracts},
year = {2022},
date = {2022-07-05},
urldate = {2022-07-05},
howpublished = {Book of Abstracts - 41th Benelux Meeting on Systems and Control},
keywords = {controllability, DAEs, piecewise-smooth-distributions, switched-DAEs, switched-systems},
pubstate = {published},
tppubtype = {misc}
}
|
Xu, Teke; Water, Alden; Trenn, Stephan Dynamical boundary conditions for the water hammer problem Miscellaneous Book of Abstracts - XVIII International Conference on Hyperbolic Problems: Theory, Numerics, and Applications (HYP 2022), 2022. @misc{XuWate22m,
title = {Dynamical boundary conditions for the water hammer problem},
author = {Teke Xu and Alden Water and Stephan Trenn},
url = {https://stephantrenn.net/wp-content/uploads/2023/02/XuWate22m.pdf, Extended Abstract},
year = {2022},
date = {2022-06-24},
howpublished = {Book of Abstracts - XVIII International Conference on Hyperbolic Problems: Theory, Numerics, and Applications (HYP 2022)},
keywords = {PDEs, solution-theory, switched-systems},
pubstate = {published},
tppubtype = {misc}
}
|
2021
|
Sutrisno,; Trenn, Stephan Observability and Determinability of Discrete Time Switched Linear Singular Systems: Multiple Switches Case Miscellaneous Book of Abstracts - 40th Benelux Workshop on Systems and Control, 2021, (extended abstract). @misc{SutrTren21m,
title = {Observability and Determinability of Discrete Time Switched Linear Singular Systems: Multiple Switches Case},
author = {Sutrisno and Stephan Trenn},
editor = {Erjen Lefeber and Julien Hendrickx},
url = {https://stephantrenn.net/wp-content/uploads/2023/01/SutrTren21m.pdf, Abstract
https://www.beneluxmeeting.nl/2021/uploads/bmsc/boa.pdf, Book of Abstracts},
year = {2021},
date = {2021-06-29},
urldate = {2021-06-29},
pages = {94-94},
address = {Rotterdam, The Netherlands},
howpublished = {Book of Abstracts - 40th Benelux Workshop on Systems and Control},
note = {extended abstract},
keywords = {DAEs, discrete-time, observability, switched-DAEs, switched-systems},
pubstate = {published},
tppubtype = {misc}
}
|
2020
|
Chen, Yahao; Trenn, Stephan On geometric and differentiation index of nonlinear differential algebraic equations Miscellaneous Book of Abstracts - 39th Benelux Meeting on Systems and Control, 2020. @misc{ChenTren20m,
title = {On geometric and differentiation index of nonlinear differential algebraic equations},
author = {Yahao Chen and Stephan Trenn},
editor = {Raffaella Carloni and Bayu Jayawardhana and Erjen Lefeber},
url = {https://www.beneluxmeeting.nl/2020/uploads/papers/boa.pdf, Book of Abstracts
https://stephantrenn.net/wp-content/uploads/2021/03/ChenTren20.pdf, Extended Abstract},
year = {2020},
date = {2020-03-12},
howpublished = {Book of Abstracts - 39th Benelux Meeting on Systems and Control},
keywords = {DAEs, nonlinear, solution-theory},
pubstate = {published},
tppubtype = {misc}
}
|
Hossain, Sumon; Trenn, Stephan Model reduction of switched systems in time-varying approach Miscellaneous Book of Abstracts - 39th Benelux Meeting on Systems and Control, 2020. @misc{HossTren20m,
title = {Model reduction of switched systems in time-varying approach},
author = {Sumon Hossain and Stephan Trenn},
editor = {Raffaella Carloni and Bayu Jayawardhana and Erjen Lefeber},
url = {https://www.beneluxmeeting.nl/2020/uploads/papers/boa.pdf, Book of Abstracts
https://stephantrenn.net/wp-content/uploads/2021/03/HossTren20.pdf, Extended Abstract},
year = {2020},
date = {2020-03-12},
howpublished = {Book of Abstracts - 39th Benelux Meeting on Systems and Control},
keywords = {model-reduction, switched-systems},
pubstate = {published},
tppubtype = {misc}
}
|
Hu, Jiaming; Trenn, Stephan Sliding mode observer based hysteresis compensation control for piezoelectric stacks Miscellaneous Book of Abstracts - 39th Benelux Meeting on Systems and Control, 2020. @misc{HuTren20m,
title = {Sliding mode observer based hysteresis compensation control for piezoelectric stacks},
author = {Jiaming Hu and Stephan Trenn},
editor = {Raffaella Carloni and Bayu Jayawardhana and Erjen Lefeber},
url = {https://www.beneluxmeeting.nl/2020/uploads/papers/boa.pdf, Book of Abstracts
https://stephantrenn.net/wp-content/uploads/2021/03/HuTren20.pdf, Extended Abstract},
year = {2020},
date = {2020-03-12},
howpublished = {Book of Abstracts - 39th Benelux Meeting on Systems and Control},
keywords = {application, nonlinear},
pubstate = {published},
tppubtype = {misc}
}
|
Wijnbergen, Paul; Trenn, Stephan A forward approach to controllability of switched DAEs Miscellaneous Book of Abstracts - 39th Benelux Meeting on Systems and Control, 2020. @misc{WijnTren20m,
title = {A forward approach to controllability of switched DAEs},
author = {Paul Wijnbergen and Stephan Trenn},
editor = {Raffaella Carloni and Bayu Jayawardhana and Erjen Lefeber},
url = {https://www.beneluxmeeting.nl/2020/uploads/papers/boa.pdf, Book of Abstracts
https://stephantrenn.net/wp-content/uploads/2021/03/WijnTren20.pdf, Extended Abstract},
year = {2020},
date = {2020-03-12},
howpublished = {Book of Abstracts - 39th Benelux Meeting on Systems and Control},
keywords = {controllability, switched-DAEs, switched-systems},
pubstate = {published},
tppubtype = {misc}
}
|
Boon, Marko; van den Bosch, Mark; Breeuwsma, Paul; Bucchianico, Alessandro Di; Emampour, Mona; van Ginkel, Bart; Hepkema, Tjebbe; Holzinger, Philipp; Timmerman, Rik; Trenn, Stephan Event Driven Model with an Objective to Control Traffic Lights in the Netherlands Miscellaneous Scientific Proceedings 157th European Study Group with Industry (SWI 2020), 2020. @misc{BoonBosc20m,
title = {Event Driven Model with an Objective to Control Traffic Lights in the Netherlands},
author = {Marko Boon and Mark van den Bosch and Paul Breeuwsma and Alessandro Di Bucchianico and Mona Emampour and Bart van Ginkel and Tjebbe Hepkema and Philipp Holzinger and Rik Timmerman and Stephan Trenn},
editor = {Bram van den Broek},
url = {https://stephantrenn.net/wp-content/uploads/2023/02/BoonBosc20m.pdf, Report
https://www.swi-wiskunde.nl/swi2020/wp-content/uploads/sites/26/2020/10/swi2020scproceedings.pdf, Proceedings SWI 2020},
year = {2020},
date = {2020-03-01},
urldate = {2020-03-01},
abstract = {The study group participants of SWI 2020 with regard to the challenge proposed by the company Sweco were tasked to initiate a discrete-event dynamic model into Smart Traffic. Smart Traffic is cloud driven software developed by Sweco, implementing real-time predictive traf- fic signal control. Currently, the microscopic traffic simulator SUMO is being used within Smart Traffic to predict the traffic pattern for the short-term future, with the purpose of optimising traffic signal settings. However, in practice, microscopic traffic simulators appear to be too slow and hence infeasible considering its application. We employ discrete-event simulations as a tool to predict the future traffic state both efficiently and effectively, even though those type of simulations are usually employed in a different context.
We were in particular advised to focus on devising an event-driven model for a single, general intersection. This enabled us to create a thorough mathematical basic model. We are able to study various performance characteristics of the traffic light, such as the total delay or to the total squared delay. Accompanied with the mathematical basic model, we deliver in correspondence a fully functioning program written in Python. Our article includes a detailed yet relatively simple example based on this program. This example additionally demonstrates the difference in an optimal outcome when using the total delay or the total squared delay. Ultimately, we note that our model is easily extendable and several feasible extensions are proposed in this article.},
howpublished = {Scientific Proceedings 157th European Study Group with Industry (SWI 2020)},
keywords = {application},
pubstate = {published},
tppubtype = {misc}
}
The study group participants of SWI 2020 with regard to the challenge proposed by the company Sweco were tasked to initiate a discrete-event dynamic model into Smart Traffic. Smart Traffic is cloud driven software developed by Sweco, implementing real-time predictive traf- fic signal control. Currently, the microscopic traffic simulator SUMO is being used within Smart Traffic to predict the traffic pattern for the short-term future, with the purpose of optimising traffic signal settings. However, in practice, microscopic traffic simulators appear to be too slow and hence infeasible considering its application. We employ discrete-event simulations as a tool to predict the future traffic state both efficiently and effectively, even though those type of simulations are usually employed in a different context.
We were in particular advised to focus on devising an event-driven model for a single, general intersection. This enabled us to create a thorough mathematical basic model. We are able to study various performance characteristics of the traffic light, such as the total delay or to the total squared delay. Accompanied with the mathematical basic model, we deliver in correspondence a fully functioning program written in Python. Our article includes a detailed yet relatively simple example based on this program. This example additionally demonstrates the difference in an optimal outcome when using the total delay or the total squared delay. Ultimately, we note that our model is easily extendable and several feasible extensions are proposed in this article. |
Iervolino, Raffaele; Vasca, Francesco; Trenn, Stephan Discontinuous Lyapunov functions for discontinous piecewise-affine systems Miscellaneous Extended Abstract, 2020, (accepted for cancelled MTNS 20/21). @misc{IervTren20m,
title = {Discontinuous Lyapunov functions for discontinous piecewise-affine systems},
author = {Raffaele Iervolino and Francesco Vasca and Stephan Trenn},
url = {https://stephantrenn.net/wp-content/uploads/2020/01/Preprint-ITV200122.pdf, Extended Abstract},
year = {2020},
date = {2020-01-22},
urldate = {2020-01-22},
abstract = {Asymptotic stability of continuous-time piecewise affine systems defined over a polyhedral partition of the state space, with possible discontinuous vector field on the boundaries, is considered. We first introduce the feasible Filippov solution concept by characterizing single-mode Caratheodory, sliding mode and forward Zeno behaviors. Then, a global asymptotic stability result through a (possibly discontinuous) piecewise Lyapunov function is presented. The sufficient conditions are based on pointwise classifications of the trajectories which allow the identification of crossing, unreachable and Caratheodory boundaries. It is highlighted that the sign and jump conditions of the stability theorem can be expressed in terms of linear matrix inequalities by particularizing to piecewise quadratic Lyapunov functions and using the cone-copositivity approach. },
howpublished = {Extended Abstract},
note = {accepted for cancelled MTNS 20/21},
keywords = {LMIs, Lyapunov, stability, switched-systems},
pubstate = {published},
tppubtype = {misc}
}
Asymptotic stability of continuous-time piecewise affine systems defined over a polyhedral partition of the state space, with possible discontinuous vector field on the boundaries, is considered. We first introduce the feasible Filippov solution concept by characterizing single-mode Caratheodory, sliding mode and forward Zeno behaviors. Then, a global asymptotic stability result through a (possibly discontinuous) piecewise Lyapunov function is presented. The sufficient conditions are based on pointwise classifications of the trajectories which allow the identification of crossing, unreachable and Caratheodory boundaries. It is highlighted that the sign and jump conditions of the stability theorem can be expressed in terms of linear matrix inequalities by particularizing to piecewise quadratic Lyapunov functions and using the cone-copositivity approach. |
Trenn, Stephan The Laplace transform and inconsistent initial values Miscellaneous Extended Abstract, 2020, (accepted for cancelled MTNS 20/21, presented at MTNS 2022). @misc{Tren20m,
title = {The Laplace transform and inconsistent initial values},
author = {Stephan Trenn},
url = {https://stephantrenn.net/wp-content/uploads/2020/01/Preprint-Tre200122.pdf, Extended Abstract},
year = {2020},
date = {2020-01-22},
urldate = {2020-01-22},
abstract = {Switches in electrical circuits may lead to Dirac impulses in the solution; a real word example utilizing this effect is the spark plug. Treating these Dirac impulses in a mathematically rigorous way is surprisingly challenging. This is in particular true for arguments made in the frequency domain in connection with the Laplace transform. A survey will be given on how inconsistent initials values have been treated in the past and how these approaches can be justified in view of the now available solution theory based on piecewise-smooth distributions.},
howpublished = {Extended Abstract},
note = {accepted for cancelled MTNS 20/21, presented at MTNS 2022},
keywords = {DAEs, piecewise-smooth-distributions, solution-theory, switched-DAEs},
pubstate = {published},
tppubtype = {misc}
}
Switches in electrical circuits may lead to Dirac impulses in the solution; a real word example utilizing this effect is the spark plug. Treating these Dirac impulses in a mathematically rigorous way is surprisingly challenging. This is in particular true for arguments made in the frequency domain in connection with the Laplace transform. A survey will be given on how inconsistent initials values have been treated in the past and how these approaches can be justified in view of the now available solution theory based on piecewise-smooth distributions. |
2010
|
Liberzon, Daniel; Trenn, Stephan The Bang-Bang Funnel Controller (long version) Miscellaneous Extended Conference Manuscript, 2010, (long version of corresponding CDC paper). @misc{LibeTren10m,
title = {The Bang-Bang Funnel Controller (long version)},
author = {Daniel Liberzon and Stephan Trenn},
url = {https://stephantrenn.net/wp-content/uploads/2017/09/Preprint-LT100806longVersion.pdf, Long version of corresponding CDC-paper},
year = {2010},
date = {2010-08-06},
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.},
howpublished = {Extended Conference Manuscript},
note = {long version of corresponding CDC paper},
keywords = {funnel-control, input-constraints, switched-systems},
pubstate = {published},
tppubtype = {misc}
}
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. |
2009
|
Trenn, Stephan Impulse free solutions for switched differential algebraic equations Miscellaneous Preprint, 2009, (After the initial submission, I decided not to revise this manuscript and instead included most of the content in the paper "Switched nonlinear differential algebraic equations: Solution theory, Lyapunov functions, and stability" (joint work with Daniel Liberzon), which appeared 2012 in Automatica.). @misc{Tren09m,
title = {Impulse free solutions for switched differential algebraic equations},
author = {Stephan Trenn},
url = {https://www.tu-ilmenau.de/fileadmin/media/math/Preprints/2009/09_03_trenn.pdf, TU-Ilmenau Preprint Server
https://stephantrenn.net/wp-content/uploads/2021/03/Preprint-Tre090123.pdf, Preprint},
year = {2009},
date = {2009-01-23},
abstract = {Linear switched differential algebraic equations (switched DAEs) are studied. First, a suitable solution space is introduced, the space of so called piecewise-smooth distributions. Secondly, sufficient conditions are given which ensure that all solutions of the switched DAE are impulse and/or jump free. These conditions are easy to check and are expressed directly in the systems original data. As an example a simple electrical circuit with a switch is analyzed.},
howpublished = {Preprint},
note = {After the initial submission, I decided not to revise this manuscript and instead included most of the content in the paper "Switched nonlinear differential algebraic equations: Solution theory, Lyapunov functions, and stability" (joint work with Daniel Liberzon), which appeared 2012 in Automatica.},
keywords = {piecewise-smooth-distributions, solution-theory, switched-DAEs, switched-systems},
pubstate = {published},
tppubtype = {misc}
}
Linear switched differential algebraic equations (switched DAEs) are studied. First, a suitable solution space is introduced, the space of so called piecewise-smooth distributions. Secondly, sufficient conditions are given which ensure that all solutions of the switched DAE are impulse and/or jump free. These conditions are easy to check and are expressed directly in the systems original data. As an example a simple electrical circuit with a switch is analyzed. |
