2024
|
Sutrisno,; Trenn, Stephan Switched linear singular systems in discrete time: Solution theory and observability notions Journal Article In: Systems & Control Letters, vol. 183, no. 105674, pp. 1-11, 2024, (open access). @article{SutrTren24,
title = {Switched linear singular systems in discrete time: Solution theory and observability notions},
author = {Sutrisno and Stephan Trenn},
url = {https://stephantrenn.net/wp-content/uploads/2023/11/SutrTren24.pdf, Paper},
doi = {10.1016/j.sysconle.2023.105674},
year = {2024},
date = {2024-01-01},
urldate = {2023-11-16},
journal = {Systems & Control Letters},
volume = {183},
number = {105674},
pages = {1-11},
abstract = {We study the solution theory of linear switched singular systems. In a recent paper by Anh et al. (2019), it was highlighted that the common assumption that each mode of the switched system is index-1 is not sufficient to guarantee existence and uniqueness of solutions of the corresponding switched system and the notion of “jointly index-1” was introduced. However, until now it was not clear what conditions are actually required to guarantee existence and uniqueness of solutions if the switching signal is not considered arbitrary. In particular, we study the two relevant situations where the mode sequence is fixed (and the switching times are arbitrary) and where the whole switching signal is fixed. In both cases, we provide conditions in terms of the original system matrices which ensure existence and uniqueness of solutions. We also extend the idea of the one-step map introduced by Anh et al. (2019) to these two cases. It turns out that in the case of a fixed switching signal, the index-1 condition for the individual modes is also not necessary (in addition to not being sufficient). Furthermore, we utilize the established solution theory to provide characterizations of observability and determinability of switched singular systems.},
note = {open access},
keywords = {DAEs, discrete-time, observability, solution-theory, switched-DAEs, switched-systems},
pubstate = {published},
tppubtype = {article}
}
We study the solution theory of linear switched singular systems. In a recent paper by Anh et al. (2019), it was highlighted that the common assumption that each mode of the switched system is index-1 is not sufficient to guarantee existence and uniqueness of solutions of the corresponding switched system and the notion of “jointly index-1” was introduced. However, until now it was not clear what conditions are actually required to guarantee existence and uniqueness of solutions if the switching signal is not considered arbitrary. In particular, we study the two relevant situations where the mode sequence is fixed (and the switching times are arbitrary) and where the whole switching signal is fixed. In both cases, we provide conditions in terms of the original system matrices which ensure existence and uniqueness of solutions. We also extend the idea of the one-step map introduced by Anh et al. (2019) to these two cases. It turns out that in the case of a fixed switching signal, the index-1 condition for the individual modes is also not necessary (in addition to not being sufficient). Furthermore, we utilize the established solution theory to provide characterizations of observability and determinability of switched singular systems. |
2023
|
Sutrisno,; Trenn, Stephan Inhomogeneous singular linear switched systems in discrete time: Solvability, reachability, and controllability Characterizations Proceedings Article In: Proc. 62nd IEEE Conf. Decision Control, pp. 5869-5874, IEEE, Singapore, 2023. @inproceedings{SutrTren23c,
title = {Inhomogeneous singular linear switched systems in discrete time: Solvability, reachability, and controllability Characterizations},
author = {Sutrisno and Stephan Trenn},
url = {https://stephantrenn.net/wp-content/uploads/2023/11/Preprint-ST230915.pdf, Preprint},
doi = {10.1109/CDC49753.2023.10384306},
year = {2023},
date = {2023-12-14},
urldate = {2023-12-14},
booktitle = {Proc. 62nd IEEE Conf. Decision Control},
pages = {5869-5874},
publisher = {IEEE},
address = {Singapore},
abstract = {In this paper we study a novel solvability notion for discrete-time singular linear switched systems with inputs. We consider the existence and uniqueness of a solution on arbitrary finite time intervals with arbitrary inputs and arbitrary switching signals, and furthermore, we pay special attention to strict causality, i.e. the current state is only allowed to depend on past values of the state and the input. A necessary and sufficient condition for this solvability notion is then established. Furthermore, a surrogate switched system (an ordinary switched system that has equivalent input-output behavior) is derived for any solvable system. By utilizing those surrogate systems, we are able to characterize the reachability and controllability properties of the original singular systems using a geometric approach.},
keywords = {controllability, DAEs, discrete-time, solution-theory, switched-DAEs, switched-systems},
pubstate = {published},
tppubtype = {inproceedings}
}
In this paper we study a novel solvability notion for discrete-time singular linear switched systems with inputs. We consider the existence and uniqueness of a solution on arbitrary finite time intervals with arbitrary inputs and arbitrary switching signals, and furthermore, we pay special attention to strict causality, i.e. the current state is only allowed to depend on past values of the state and the input. A necessary and sufficient condition for this solvability notion is then established. Furthermore, a surrogate switched system (an ordinary switched system that has equivalent input-output behavior) is derived for any solvable system. By utilizing those surrogate systems, we are able to characterize the reachability and controllability properties of the original singular systems using a geometric approach. |
Sutrisno,; Yin, Hao; Trenn, Stephan; Jayawardhana, Bayu Nonlinear singular switched systems in discrete-time: solution theory and incremental stability under restricted switching signals Proceedings Article In: Proc. 62nd IEEE Conf. Decision Control, pp. 914-919, IEEE, Singapore, 2023. @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}
}
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. |
Lanza, Lukas; Dennstädt, Dario; Worthmann, Karl; Schmitz, Philipp; Sen, Gökcen Devlet; Trenn, Stephan; Schaller, Manuel Control and safe continual learning of output-constrained nonlinear systems Unpublished 2023, (submitted). @unpublished{LanzDann23pp,
title = {Control and safe continual learning of output-constrained nonlinear systems},
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/2023/12/Preprint-LDWSSTS231212.pdf, Preprint
https://arxiv.org/abs/2303.00523, arXiv},
year = {2023},
date = {2023-12-12},
urldate = {2023-03-01},
abstract = {We propose a novel learning-based tracking controller for nonlinear systems of arbitrary relative degree. Here, we use sample-and-hold input signals and derive a bound on the required sampling frequency. While the controller guarantees tracking within prescribed, possibly time-varying bounds on the error signal, system data is collected at runtime to continuously improve the controller performance. Furthermore, a safe region is defined, in which the control signal can even be used to (persistently) excite the system and, thus, to enhance the learning outcome. A particular strength is the flexibility to incorporate different learning paradigms, e.g., reinforcement learning or non-parametric predictive controllers based on Willems et al.’s so-called fundamental lemma, which is demonstrated by numerical simulations.},
note = {submitted},
keywords = {discrete-time, funnel-control, input-constraints, relative-degree},
pubstate = {published},
tppubtype = {unpublished}
}
We propose a novel learning-based tracking controller for nonlinear systems of arbitrary relative degree. Here, we use sample-and-hold input signals and derive a bound on the required sampling frequency. While the controller guarantees tracking within prescribed, possibly time-varying bounds on the error signal, system data is collected at runtime to continuously improve the controller performance. Furthermore, a safe region is defined, in which the control signal can even be used to (persistently) excite the system and, thus, to enhance the learning outcome. A particular strength is the flexibility to incorporate different learning paradigms, e.g., reinforcement learning or non-parametric predictive controllers based on Willems et al.’s so-called fundamental lemma, which is demonstrated by numerical simulations. |
Sutrisno,; Trenn, Stephan Nonlinear switched singular systems in discrete-time: The one-step map and stability under arbitrary switching signals Journal Article In: European Journal of Control, vol. 74, no. 100852, pp. 1-7, 2023, (presented at the 2023 European Control Conference, Bucharest, Rumania; open access). @article{SutrTren23a,
title = {Nonlinear switched singular systems in discrete-time: The one-step map and stability under arbitrary switching signals},
author = {Sutrisno and Stephan Trenn},
url = {https://stephantrenn.net/wp-content/uploads/2024/02/SutrTren23a.pdf, Paper},
doi = {10.1016/j.ejcon.2023.100852},
year = {2023},
date = {2023-11-01},
urldate = {2023-11-01},
journal = {European Journal of Control},
volume = {74},
number = {100852},
pages = {1-7},
abstract = {The solvability of nonlinear nonswitched and switched singular systems in discrete time is studied. We provide necessary and sufficient conditions for solvability. The one-step map that generates equivalent nonlinear (ordinary) systems for solvable nonlinear singular systems under arbitrary switching signals is introduced. Moreover, the stability is studied by utilizing this one-step map. A sufficient condition for stability is provided in terms of (switched) Lyapunov functions.},
note = {presented at the 2023 European Control Conference, Bucharest, Rumania; open access},
keywords = {DAEs, discrete-time, nonlinear, solution-theory, stability, switched-DAEs, switched-systems},
pubstate = {published},
tppubtype = {article}
}
The solvability of nonlinear nonswitched and switched singular systems in discrete time is studied. We provide necessary and sufficient conditions for solvability. The one-step map that generates equivalent nonlinear (ordinary) systems for solvable nonlinear singular systems under arbitrary switching signals is introduced. Moreover, the stability is studied by utilizing this one-step map. A sufficient condition for stability is provided in terms of (switched) Lyapunov functions. |
Sutrisno,; Trenn, Stephan Reachability and Controllability Characterizations for Linear Switched Systems in Discrete Time: A Geometric Approach Proceedings Article In: Proc. 2023 European Control Conference (ECC), pp. 2227-2232, Bucharest, Rumania , 2023. @inproceedings{SutrTren23b,
title = {Reachability and Controllability Characterizations for Linear Switched Systems in Discrete Time: A Geometric Approach},
author = {Sutrisno and Stephan Trenn},
url = {https://stephantrenn.net/wp-content/uploads/2022/11/Preprint-ST221125a.pdf, Preprint},
doi = {10.23919/ECC57647.2023.10178124},
year = {2023},
date = {2023-06-13},
urldate = {2023-06-13},
booktitle = {Proc. 2023 European Control Conference (ECC)},
pages = {2227-2232},
address = {Bucharest, Rumania },
abstract = {This article presents the reachability and controllability characterizations for discrete-time linear switched systems under a fixed and known switching signal. A geometric approach is used, and we are able to provide alternative conditions which are more computationally friendly compared to existing results by utilizing the solution formula at switching times. Furthermore, the proposed conditions make it easier to study the dependency of the reachability and controllability on the switching times and the mode sequences; this is a new result currently not investigated in the literature. Some academic examples are provided to illustrate the novel features found in this study.},
keywords = {controllability, discrete-time, switched-systems},
pubstate = {published},
tppubtype = {inproceedings}
}
This article presents the reachability and controllability characterizations for discrete-time linear switched systems under a fixed and known switching signal. A geometric approach is used, and we are able to provide alternative conditions which are more computationally friendly compared to existing results by utilizing the solution formula at switching times. Furthermore, the proposed conditions make it easier to study the dependency of the reachability and controllability on the switching times and the mode sequences; this is a new result currently not investigated in the literature. Some academic examples are provided to illustrate the novel features found in this study. |
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. |
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}
}
|
2021
|
Sutrisno,; Trenn, Stephan Observability and Determinability Characterizations for Linear Switched Systems in Discrete Time Proceedings Article In: Proc. 60th IEEE Conf. Decision and Control (CDC 2021), pp. 2474-2479, 2021. @inproceedings{SutrTren21b,
title = {Observability and Determinability Characterizations for Linear Switched Systems in Discrete Time},
author = {Sutrisno and Stephan Trenn},
url = {https://stephantrenn.net/wp-content/uploads/2021/09/Preprint-ST210907.pdf, Preprint},
doi = {10.1109/CDC45484.2021.9682894},
year = {2021},
date = {2021-09-07},
urldate = {2021-09-07},
booktitle = {Proc. 60th IEEE Conf. Decision and Control (CDC 2021)},
pages = {2474-2479},
abstract = {In this article, we study the observability and determinability for discrete-time linear switched systems. Studies for the observability for this system class are already available in literature, however, we use assume here that the switching signal is known. This leads to less conservative observability conditions (e.g. observability of each individual mode is not necessary for the overall switched system to be observable); in particular, the dependencies of observability on the switching times and the mode sequences are derived; these results are currently not available in the literature on discrete-time switched systems. In addition to observability (which is concerned with recovering the state from the initial time onwards), we also investigate the determinability which is concerned with the ability to reconstruct the state value at the end of the observation interval. We provide several simple examples to illustrate novel features not seen in the continuous time case or for unswitched systems.},
keywords = {discrete-time, observability, switched-systems},
pubstate = {published},
tppubtype = {inproceedings}
}
In this article, we study the observability and determinability for discrete-time linear switched systems. Studies for the observability for this system class are already available in literature, however, we use assume here that the switching signal is known. This leads to less conservative observability conditions (e.g. observability of each individual mode is not necessary for the overall switched system to be observable); in particular, the dependencies of observability on the switching times and the mode sequences are derived; these results are currently not available in the literature on discrete-time switched systems. In addition to observability (which is concerned with recovering the state from the initial time onwards), we also investigate the determinability which is concerned with the ability to reconstruct the state value at the end of the observation interval. We provide several simple examples to illustrate novel features not seen in the continuous time case or for unswitched systems. |
Sutrisno,; Trenn, Stephan Observability of Singular Linear Switched Systems in Discrete Time: Single Switch Case Proceedings Article In: Proc. European Control Conference (ECC21), pp. 267-292, Rotterdam, Netherlands, 2021. @inproceedings{SutrTren21a,
title = {Observability of Singular Linear Switched Systems in Discrete Time: Single Switch Case},
author = {Sutrisno and Stephan Trenn},
url = {https://stephantrenn.net/wp-content/uploads/2021/04/Preprint-ST210406.pdf, Preprint},
doi = {10.23919/ECC54610.2021.9654844},
year = {2021},
date = {2021-06-29},
urldate = {2021-06-29},
booktitle = {Proc. European Control Conference (ECC21)},
pages = {267-292},
address = {Rotterdam, Netherlands},
abstract = {In this paper, we investigate the observability of singular linear switched systems in discrete time. As a preliminary study, we restrict ourselves to systems with a single switch switching signal, i.e. the system switches from one mode to another mode at a certain switching time. We provide two necessary and sufficient conditions for the observability characterization. The first condition is applied for arbitrary switching time and the second one is for switching times that are far enough from the initial time and the final time of observation. These two conditions explicitly contain the switching time variable that indicates that in general, the observability is dependent on the switching time. However, under some sufficient conditions we provide, the observability will not depend on the switching time anymore. Furthermore, the observability of systems with two-dimensional states is inde- pendent of the switching time. In addition, from the example we discussed, an observable switched system can be built from two unobservable modes and different mode sequences may produce different observability property; in particular, swapping the mode sequence may destroy observability.},
keywords = {discrete-time, observability, switched-systems},
pubstate = {published},
tppubtype = {inproceedings}
}
In this paper, we investigate the observability of singular linear switched systems in discrete time. As a preliminary study, we restrict ourselves to systems with a single switch switching signal, i.e. the system switches from one mode to another mode at a certain switching time. We provide two necessary and sufficient conditions for the observability characterization. The first condition is applied for arbitrary switching time and the second one is for switching times that are far enough from the initial time and the final time of observation. These two conditions explicitly contain the switching time variable that indicates that in general, the observability is dependent on the switching time. However, under some sufficient conditions we provide, the observability will not depend on the switching time anymore. Furthermore, the observability of systems with two-dimensional states is inde- pendent of the switching time. In addition, from the example we discussed, an observable switched system can be built from two unobservable modes and different mode sequences may produce different observability property; in particular, swapping the mode sequence may destroy observability. |
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
|
Anh, Pham Ky; Linh, Pham Thi; Thuan, Do Duc; Trenn, Stephan Stability analysis for switched discrete-time linear singular systems Journal Article In: Automatica, vol. 119, no. 109100, 2020. @article{AnhLinh20,
title = {Stability analysis for switched discrete-time linear singular systems},
author = {Pham Ky Anh and Pham Thi Linh and Do Duc Thuan and Stephan Trenn},
url = {https://stephantrenn.net/wp-content/uploads/2020/02/Preprint-ALTT200515.pdf, Preprint},
doi = {10.1016/j.automatica.2020.109100},
year = {2020},
date = {2020-09-01},
urldate = {2020-09-01},
journal = {Automatica},
volume = {119},
number = {109100},
abstract = {The stability of arbitrarily switched discrete-time linear singular (SDLS) systems is studied. Our analysis builds on the recently introduced one-step-map for SDLS systems of index-1. We first provide a sufficient stability conditions in terms of Lyapunov functions. Furthermore, we generalize the notion of joint spectral radius of a finite set of matrix pairs, which allows us to fully characterize exponential stability.},
keywords = {discrete-time, stability, switched-systems},
pubstate = {published},
tppubtype = {article}
}
The stability of arbitrarily switched discrete-time linear singular (SDLS) systems is studied. Our analysis builds on the recently introduced one-step-map for SDLS systems of index-1. We first provide a sufficient stability conditions in terms of Lyapunov functions. Furthermore, we generalize the notion of joint spectral radius of a finite set of matrix pairs, which allows us to fully characterize exponential stability. |
2019
|
Anh, Pham Ky; Linh, Pham Thi; Thuan, Do Duc; Trenn, Stephan The one-step-map for switched singular systems in discrete-time Proceedings Article In: Proc. 58th IEEE Conf. Decision Control (CDC) 2019, pp. 605-610, Nice, France, 2019. @inproceedings{AnhLinh19,
title = {The one-step-map for switched singular systems in discrete-time},
author = {Pham Ky Anh and Pham Thi Linh and Do Duc Thuan and Stephan Trenn},
url = {https://stephantrenn.net/wp-content/uploads/2019/03/Preprint-ALTT190910.pdf, Preprint},
doi = {10.1109/CDC40024.2019.9030154},
year = {2019},
date = {2019-12-11},
urldate = {2019-12-11},
booktitle = {Proc. 58th IEEE Conf. Decision Control (CDC) 2019},
pages = {605-610},
address = {Nice, France},
abstract = {We study switched singular systems in discrete time and first highlight that in contrast to continuous time regularity of the corresponding matrix pairs is not sufficient to ensure a solution behavior which is causal with respect to the switching signal. With a suitable index-1 assumption for the whole switched system, we are able to define a one-step- map which can be used to provide explicit solution formulas for general switching signals.},
keywords = {discrete-time, solution-theory, switched-systems},
pubstate = {published},
tppubtype = {inproceedings}
}
We study switched singular systems in discrete time and first highlight that in contrast to continuous time regularity of the corresponding matrix pairs is not sufficient to ensure a solution behavior which is causal with respect to the switching signal. With a suitable index-1 assumption for the whole switched system, we are able to define a one-step- map which can be used to provide explicit solution formulas for general switching signals. |
