2024
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Hossain, Sumon; Trenn, Stephan Midpoint based balanced truncation for switched linear systems with known switching signal Journal Article In: IEEE Transactions on Automatic Control, vol. 69, no. 1, 2024, (2023 early access). @article{HossTren24,
title = {Midpoint based balanced truncation for switched linear systems with known switching signal},
author = {Sumon Hossain and Stephan Trenn},
url = {https://stephantrenn.net/wp-content/uploads/2023/05/Preprint-HT230508.pdf, Preprint},
doi = {10.1109/TAC.2023.3269721},
year = {2024},
date = {2024-01-01},
urldate = {2024-01-01},
journal = {IEEE Transactions on Automatic Control},
volume = {69},
number = {1},
abstract = {We propose a novel model reduction approach for switched linear systems with known switching signal. The class of considered systems encompasses switched systems with mode-dependent state-dimension as well as impulsive systems. Our method is based on a suitable definition of (time-varying) reachability and observability Gramians and we show that these Gramians satisfy precise interpretations in terms of input and output energy. Based on balancing the midpoint Gramians, we propose a piecewise-constant projection based model reduction resulting in a switched linear system of smaller size.},
note = {2023 early access},
keywords = {controllability, model-reduction, observability, switched-systems},
pubstate = {published},
tppubtype = {article}
}
We propose a novel model reduction approach for switched linear systems with known switching signal. The class of considered systems encompasses switched systems with mode-dependent state-dimension as well as impulsive systems. Our method is based on a suitable definition of (time-varying) reachability and observability Gramians and we show that these Gramians satisfy precise interpretations in terms of input and output energy. Based on balancing the midpoint Gramians, we propose a piecewise-constant projection based model reduction resulting in a switched linear system of smaller size. |
2023
|
Hossain, Sumon; Trenn, Stephan Reduced realization for switched linear systems with known mode sequence Journal Article In: Automatica, vol. 154, no. 111065, pp. 1-9, 2023, (open access). @article{HossTren23a,
title = {Reduced realization for switched linear systems with known mode sequence},
author = {Sumon Hossain and Stephan Trenn},
url = {https://stephantrenn.net/wp-content/uploads/2023/03/Preprint-HT230322.pdf, Preprint
https://doi.org/10.5281/zenodo.6410136, Matlab sources},
doi = {10.1016/j.automatica.2023.111065},
year = {2023},
date = {2023-03-22},
urldate = {2023-03-22},
journal = {Automatica},
volume = {154},
number = {111065},
pages = {1-9},
abstract = {We consider switched linear systems with mode-dependent state-dimensions and/or state jumps and propose a method to obtain a switched system of reduced size with identical input-output behavior. Our approach is based in considering time-dependent reachability and unobservability spaces as well as suitable extended reachability and restricted unobservability spaces together with the notion of a weak Kalman decomposition. A key feature of our approach is that only the mode sequence of the switching signal needs to be known and not the exact switching times. However, the size of a minimal realization will in general depend on the mode durations, hence it cannot be expected that our method always leads to minimal realization. Nevertheless, we show that our method is optimal in the sense that a repeated application doesn’t lead to a further reduction and we also highlight a practically relevant special case, where minimality is achieved.},
note = {open access},
keywords = {controllability, model-reduction, observability, open-access, switched-systems},
pubstate = {published},
tppubtype = {article}
}
We consider switched linear systems with mode-dependent state-dimensions and/or state jumps and propose a method to obtain a switched system of reduced size with identical input-output behavior. Our approach is based in considering time-dependent reachability and unobservability spaces as well as suitable extended reachability and restricted unobservability spaces together with the notion of a weak Kalman decomposition. A key feature of our approach is that only the mode sequence of the switching signal needs to be known and not the exact switching times. However, the size of a minimal realization will in general depend on the mode durations, hence it cannot be expected that our method always leads to minimal realization. Nevertheless, we show that our method is optimal in the sense that a repeated application doesn’t lead to a further reduction and we also highlight a practically relevant special case, where minimality is achieved. |
2022
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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, open-access, 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. |
Hossain, Sumon; Trenn, Stephan A weak Kalman decomposition approach for reduced realizations of switched linear systems Proceedings Article In: IFAC-PapersOnLine, pp. 157-162, 2022, (Part of special issue: 10th Vienna International Conference on Mathematical Modelling MATHMOD 2022: Vienna Austria, 27–29 July 2022). @inproceedings{HossTren22,
title = {A weak Kalman decomposition approach for reduced realizations of switched linear systems},
author = {Sumon Hossain and Stephan Trenn},
url = {https://stephantrenn.net/wp-content/uploads/2022/06/Preprint-HT220613.pdf, Preprint},
doi = {10.1016/j.ifacol.2022.09.088},
year = {2022},
date = {2022-07-27},
urldate = {2022-07-27},
booktitle = {IFAC-PapersOnLine},
volume = {55},
number = {20},
pages = {157-162},
abstract = {We propose a novel reduction approach for switched linear systems with a fixed mode sequence based on subspaces related to the (time-varying) reachable and unobservable spaces. These subspaces are defined in such a way that they can be used to construct a weak Kalman decomposition, which is then in turn used to define a reduced switched linear system with an identical input-output behavior. The proposed method is illustrated with a low dimensional academic example.},
note = {Part of special issue: 10th Vienna International Conference on Mathematical Modelling MATHMOD 2022: Vienna Austria, 27–29 July 2022},
keywords = {controllability, model-reduction, observability, switched-systems},
pubstate = {published},
tppubtype = {inproceedings}
}
We propose a novel reduction approach for switched linear systems with a fixed mode sequence based on subspaces related to the (time-varying) reachable and unobservable spaces. These subspaces are defined in such a way that they can be used to construct a weak Kalman decomposition, which is then in turn used to define a reduced switched linear system with an identical input-output behavior. The proposed method is illustrated with a low dimensional academic example. |
2021
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Hossain, Sumon; Trenn, Stephan Minimality of Linear Switched Systems with known switching signal Proceedings Article In: Proceedings in Applied Mathematics and Mechanics, pp. 1-3, 2021, (open access). @inproceedings{HossTren21a,
title = {Minimality of Linear Switched Systems with known switching signal},
author = {Sumon Hossain and Stephan Trenn},
url = {https://stephantrenn.net/wp-content/uploads/2022/08/HossTren21a.pdf, Paper},
doi = {10.1002/pamm.202100067},
year = {2021},
date = {2021-12-14},
urldate = {2021-12-14},
booktitle = {Proceedings in Applied Mathematics and Mechanics},
volume = {21},
number = {e202100067},
pages = {1-3},
abstract = {Minimal realization is discussed for linear switched systems with a given switching signal. We propose a consecutive forward and backward approach for the time-interval of interest. The forward approach refers to extending the reachable subspace at each switching time by taking into account the nonzero reachable space from the previous mode. Afterwards, the backward approach extends the observable subspace of the current mode by taking observability information from the next mode into account. This results in an overall reduced switched system which is minimal and has the same input-output behavior as original system. Some examples are provided to illustrate the approach.},
note = {open access},
keywords = {controllability, model-reduction, observability, open-access, switched-systems},
pubstate = {published},
tppubtype = {inproceedings}
}
Minimal realization is discussed for linear switched systems with a given switching signal. We propose a consecutive forward and backward approach for the time-interval of interest. The forward approach refers to extending the reachable subspace at each switching time by taking into account the nonzero reachable space from the previous mode. Afterwards, the backward approach extends the observable subspace of the current mode by taking observability information from the next mode into account. This results in an overall reduced switched system which is minimal and has the same input-output behavior as original system. Some examples are provided to illustrate the approach. |
2020
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Hossain, Sumon; Trenn, Stephan A time-varying Gramian based model reduction approach for Linear Switched Systems Proceedings Article In: IFAC PapersOnline 53-2, pp. 5629-5634, 2020, (Proc. IFAC World Congress 2020, Berlin, Germany. Open access.). @inproceedings{HossTren20a,
title = {A time-varying Gramian based model reduction approach for Linear Switched Systems},
author = {Sumon Hossain and Stephan Trenn},
url = {https://stephantrenn.net/wp-content/uploads/2021/06/HossTren20a.pdf, Paper (open access)},
doi = {10.1016/j.ifacol.2020.12.1580},
year = {2020},
date = {2020-07-05},
urldate = {2020-07-05},
booktitle = {IFAC PapersOnline 53-2},
pages = {5629-5634},
abstract = {We propose a model reduction approach for switched linear system based on a balanced truncation reduction method for linear time-varying systems. The key idea is to approximate the piecewise-constant coefficient matrices with continuous time-varying coefficients and then apply available balance truncation methods for (continuous) time-varying systems. The proposed method is illustrated with a low dimensional academic example.},
note = {Proc. IFAC World Congress 2020, Berlin, Germany. Open access.},
keywords = {model-reduction, open-access, switched-systems},
pubstate = {published},
tppubtype = {inproceedings}
}
We propose a model reduction approach for switched linear system based on a balanced truncation reduction method for linear time-varying systems. The key idea is to approximate the piecewise-constant coefficient matrices with continuous time-varying coefficients and then apply available balance truncation methods for (continuous) time-varying systems. The proposed method is illustrated with a low dimensional academic example. |
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}
}
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