Patil, Deepak; Tesi, Pietro; Trenn, Stephan Indiscernible topological variations in DAE networks Journal Article In: Automatica, vol. 101, pp. 280-289, 2019. @article{PatiTesi19,
title = {Indiscernible topological variations in DAE networks},
author = {Deepak Patil and Pietro Tesi and Stephan Trenn},
url = {https://stephantrenn.net/wp-content/uploads/2019/01/Preprint-PTT181205.pdf, Preprint},
doi = {10.1016/j.automatica.2018.12.012},
year = {2019},
date = {2019-03-01},
journal = {Automatica},
volume = {101},
pages = {280-289},
abstract = {A problem of characterizing conditions under which a topological change in a network of differential algebraic equations (DAEs) can go undetected is considered. It is shown that initial conditions for which topological changes are indiscernible belong to a generalized eigenspace shared by the nominal system and the system resulting from a topological change. A condition in terms of eigenvectors of the nominal system is derived to check for existence of possibly indiscernible topological changes. For homogenous networks this condition simplifies to the existence of an eigenvector of the Laplacian of network having equal components. Lastly, a rank condition is derived which can be used to check if a topological change preserves regularity of the nominal network.},
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A problem of characterizing conditions under which a topological change in a network of differential algebraic equations (DAEs) can go undetected is considered. It is shown that initial conditions for which topological changes are indiscernible belong to a generalized eigenspace shared by the nominal system and the system resulting from a topological change. A condition in terms of eigenvectors of the nominal system is derived to check for existence of possibly indiscernible topological changes. For homogenous networks this condition simplifies to the existence of an eigenvector of the Laplacian of network having equal components. Lastly, a rank condition is derived which can be used to check if a topological change preserves regularity of the nominal network. |
Tanwani, Aneel; Trenn, Stephan Detectability and observer design for switched differential algebraic equations Journal Article In: Automatica, vol. 99, pp. 289-300, 2019. @article{TanwTren19,
title = {Detectability and observer design for switched differential algebraic equations},
author = {Aneel Tanwani and Stephan Trenn},
url = {https://stephantrenn.net/wp-content/uploads/2018/09/Preprint-TT180917.pdf, Preprint},
doi = {10.1016/j.automatica.2018.10.043},
year = {2019},
date = {2019-01-01},
journal = {Automatica},
volume = {99},
pages = {289-300},
abstract = {This paper studies detectability for switched linear differential–algebraic equations (DAEs) and its application to the synthesis of observers, which generate asymptotically converging state estimates. Equating detectability to asymptotic stability of zero-output-constrained state trajectories, and building on our work on interval-wise observability, we propose the notion of interval-wise detectability: If the output of the system is constrained to be identically zero over an interval, then the norm of the corresponding state trajectories scales down by a certain factor at the end of that interval. Conditions are provided under which the interval-wise detectability leads to asymptotic stability of zero-output-constrained state trajectories. An application is demonstrated in designing state estimators. Decomposing the state into observable and unobservable components, we show that if the observable component of the system is reset appropriately and persistently, then the estimation error converges to zero asymptotically under the interval-wise detectability assumption.},
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This paper studies detectability for switched linear differential–algebraic equations (DAEs) and its application to the synthesis of observers, which generate asymptotically converging state estimates. Equating detectability to asymptotic stability of zero-output-constrained state trajectories, and building on our work on interval-wise observability, we propose the notion of interval-wise detectability: If the output of the system is constrained to be identically zero over an interval, then the norm of the corresponding state trajectories scales down by a certain factor at the end of that interval. Conditions are provided under which the interval-wise detectability leads to asymptotic stability of zero-output-constrained state trajectories. An application is demonstrated in designing state estimators. Decomposing the state into observable and unobservable components, we show that if the observable component of the system is reset appropriately and persistently, then the estimation error converges to zero asymptotically under the interval-wise detectability assumption. |
Küsters, Ferdinand; Trenn, Stephan Switch observability for switched linear systems Journal Article In: Automatica, vol. 87, pp. 121-127, 2018. @article{KustTren18,
title = {Switch observability for switched linear systems},
author = {Ferdinand Küsters and Stephan Trenn},
url = {http://stephantrenn.net/wp-content/uploads/2017/10/Preprint-KT170808.pdf, Preprint},
doi = {https://doi.org/10.1016/j.automatica.2017.09.024},
year = {2018},
date = {2018-01-01},
journal = {Automatica},
volume = {87},
pages = {121-127},
abstract = {Mode observability of switched systems requires observability of each individual mode. We consider other concepts of observability that do not have this requirement: Switching time observability and switch observability. The latter notion is based on the assumption that at least one switch occurs. These concepts are analyzed and characterized both for homogeneous and inhomogeneous systems.},
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Mode observability of switched systems requires observability of each individual mode. We consider other concepts of observability that do not have this requirement: Switching time observability and switch observability. The latter notion is based on the assumption that at least one switch occurs. These concepts are analyzed and characterized both for homogeneous and inhomogeneous systems. |
Küsters, Ferdinand; Patil, Deepak; Trenn, Stephan Switch observability for a class of inhomogeneous switched DAEs Proceedings Article In: Proc. 56th IEEE Conf. Decis. Control, pp. 3175 - 3180, Melbourne, Australia, 2017. @inproceedings{KustPati17b,
title = {Switch observability for a class of inhomogeneous switched DAEs},
author = {Ferdinand Küsters and Deepak Patil and Stephan Trenn},
url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-KPT170919.pdf, Preprint},
doi = {10.1109/CDC.2017.8264124},
year = {2017},
date = {2017-12-13},
booktitle = {Proc. 56th IEEE Conf. Decis. Control},
pages = {3175 - 3180},
address = {Melbourne, Australia},
abstract = {Necessary and sufficient conditions for switching time and switch observability of a class of inhomogeneous switched differential algebraic equations (DAEs) are obtained. A characterization of initial states and inputs for which switched DAEs are switch unobservable is also provided by using the zeros of an augmented system obtained by combining the output of two modes suitably.},
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Necessary and sufficient conditions for switching time and switch observability of a class of inhomogeneous switched differential algebraic equations (DAEs) are obtained. A characterization of initial states and inputs for which switched DAEs are switch unobservable is also provided by using the zeros of an augmented system obtained by combining the output of two modes suitably. |
Küsters, Ferdinand; Trenn, Stephan; Wirsen, Andreas Switch-observer for switched linear systems Proceedings Article In: Proc. 56th IEEE Conf. Decis. Control, pp. 1749 - 1754, Melbourne, Australia, 2017. @inproceedings{KustTren17b,
title = {Switch-observer for switched linear systems},
author = {Ferdinand Küsters and Stephan Trenn and Andreas Wirsen},
url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-KTW170901.pdf, Preprint},
doi = {10.1109/CDC.2017.8263903},
year = {2017},
date = {2017-12-12},
booktitle = {Proc. 56th IEEE Conf. Decis. Control},
pages = {1749 - 1754},
address = {Melbourne, Australia},
abstract = {To determine the switching signal and the state of a switched linear system, one usually requires mode observability. This requires that all individual modes are observable and that the modes are distinguishable. In theory, it allows to determine the active mode in an arbitrarily short time. If one enlarges the observation to an interval that contains a switch, both assumptions (observability of each mode and clearly distinct dynamics) can be relaxed. In [Küsters and Trenn 2017] this concept, called switch observability, was formalized. It is of particular interest for fault identification. Based on switch observability, we propose an observer. This observer combines the information obtained before and after a switching instant to determine both the state and the switching signal. It is analyzed and illustrated in an example.},
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To determine the switching signal and the state of a switched linear system, one usually requires mode observability. This requires that all individual modes are observable and that the modes are distinguishable. In theory, it allows to determine the active mode in an arbitrarily short time. If one enlarges the observation to an interval that contains a switch, both assumptions (observability of each mode and clearly distinct dynamics) can be relaxed. In [Küsters and Trenn 2017] this concept, called switch observability, was formalized. It is of particular interest for fault identification. Based on switch observability, we propose an observer. This observer combines the information obtained before and after a switching instant to determine both the state and the switching signal. It is analyzed and illustrated in an example. |
Küsters, Ferdinand; Trenn, Stephan; Wirsen, Andreas Switch observability for homogeneous switched DAEs Proceedings Article In: Proc. 20th IFAC World Congress 2017, pp. 9355 - 9360, Toulouse, France, 2017, ISSN: 2405-8963. @inproceedings{KustTren17a,
title = {Switch observability for homogeneous switched DAEs},
author = {Ferdinand Küsters and Stephan Trenn and Andreas Wirsen},
url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-KTW170315.pdf, Preprint},
doi = {10.1016/j.ifacol.2017.08.1434},
issn = {2405-8963},
year = {2017},
date = {2017-03-25},
booktitle = {Proc. 20th IFAC World Congress 2017},
journal = {IFAC-PapersOnLine},
volume = {50},
number = {1},
pages = {9355 - 9360},
address = {Toulouse, France},
abstract = {We introduce the notions of switching time observability and switch observability for homogeneous switched differential-algebraic equations (DAEs). In contrast to mode detection, they do not require observability of the individual modes and are thus more suitable for fault detection and identification. Based on results in (Küsters and Trenn, 2017) for switched ordinary differential equations (ODEs), we characterize these notions for homogeneous switched DAEs and propose an observer for switch observable systems.},
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We introduce the notions of switching time observability and switch observability for homogeneous switched differential-algebraic equations (DAEs). In contrast to mode detection, they do not require observability of the individual modes and are thus more suitable for fault detection and identification. Based on results in (Küsters and Trenn, 2017) for switched ordinary differential equations (ODEs), we characterize these notions for homogeneous switched DAEs and propose an observer for switch observable systems. |
Küsters, Ferdinand; Patil, Deepak; Tesi, Pietro; Trenn, Stephan Indiscernible topological variations in DAE networks with applications to power grids Proceedings Article In: Proc. 20th IFAC World Congress 2017, pp. 7333 - 7338, Toulouse, France, 2017, ISSN: 2405-8963. @inproceedings{KustPati17a,
title = {Indiscernible topological variations in DAE networks with applications to power grids},
author = {Ferdinand Küsters and Deepak Patil and Pietro Tesi and Stephan Trenn},
url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-KPTT170320.pdf, Preprint},
doi = {10.1016/j.ifacol.2017.08.1478},
issn = {2405-8963},
year = {2017},
date = {2017-03-24},
booktitle = {Proc. 20th IFAC World Congress 2017},
journal = {IFAC-PapersOnLine},
volume = {50},
number = {1},
pages = {7333 - 7338},
address = {Toulouse, France},
abstract = {The ability to detect topology variations in dynamical networks defined by differential algebraic equations (DAEs) is considered. We characterize the existence of initial states, for which topological changes are indiscernible. A key feature of our characterization is the ability to verify indiscernibility just in terms of the nominal topology. We apply the results to a power grid model and also discuss the relationship to recent mode-detection results for switched DAEs.},
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The ability to detect topology variations in dynamical networks defined by differential algebraic equations (DAEs) is considered. We characterize the existence of initial states, for which topological changes are indiscernible. A key feature of our characterization is the ability to verify indiscernibility just in terms of the nominal topology. We apply the results to a power grid model and also discuss the relationship to recent mode-detection results for switched DAEs. |
Tanwani, Aneel; Trenn, Stephan Observer design for detectable switched differential-algebraic equations Proceedings Article In: Proc. 20th IFAC World Congress 2017, pp. 2953 - 2958, Toulouse, France, 2017, ISSN: 2405-8963. @inproceedings{TanwTren17b,
title = {Observer design for detectable switched differential-algebraic equations},
author = {Aneel Tanwani and Stephan Trenn},
url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-TT170320.pdf, Preprint},
doi = {10.1016/j.ifacol.2017.08.659},
issn = {2405-8963},
year = {2017},
date = {2017-03-22},
booktitle = {Proc. 20th IFAC World Congress 2017},
journal = {IFAC-PapersOnLine},
volume = {50},
number = {1},
pages = {2953 - 2958},
address = {Toulouse, France},
abstract = {This paper studies detectability for switched linear differential-algebraic equations (DAEs) and its application in synthesis of observers. Equating detectability to asymptotic stability of zero-output-constrained state trajectories, and building on our work on interval-wise observability, we propose the notion of interval-wise detectability: If the output of the system is constrained to be identically zero over an interval, then the norm of the corresponding state trajectories scales down by a certain factor over that interval. Conditions are provided under which the interval-wise detectability leads to asymptotic stability of zero-output-constrained state trajectories. An application is demonstrated in designing state estimators. Decomposing the state into observable and unobservable components, we show that if the observable component in the estimator is reset appropriately and persistently, then the estimation error converges to zero asymptotically under the interval-wise detectability assumption.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
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This paper studies detectability for switched linear differential-algebraic equations (DAEs) and its application in synthesis of observers. Equating detectability to asymptotic stability of zero-output-constrained state trajectories, and building on our work on interval-wise observability, we propose the notion of interval-wise detectability: If the output of the system is constrained to be identically zero over an interval, then the norm of the corresponding state trajectories scales down by a certain factor over that interval. Conditions are provided under which the interval-wise detectability leads to asymptotic stability of zero-output-constrained state trajectories. An application is demonstrated in designing state estimators. Decomposing the state into observable and unobservable components, we show that if the observable component in the estimator is reset appropriately and persistently, then the estimation error converges to zero asymptotically under the interval-wise detectability assumption. |
Tanwani, Aneel; Trenn, Stephan Determinability and state estimation for switched differential–algebraic equations Journal Article In: Automatica, vol. 76, pp. 17–31, 2017, ISSN: 0005-1098. @article{TanwTren17,
title = {Determinability and state estimation for switched differential–algebraic equations},
author = {Aneel Tanwani and Stephan Trenn},
url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-TT160919.pdf, Preprint},
doi = {10.1016/j.automatica.2016.10.024},
issn = {0005-1098},
year = {2017},
date = {2017-02-01},
journal = {Automatica},
volume = {76},
pages = {17--31},
abstract = {The problem of state reconstruction and estimation is considered for a class of switched dynamical systems whose subsystems are modeled using linear differential–algebraic equations (DAEs). Since this system class imposes time-varying dynamic and static (in the form of algebraic constraints) relations on the evolution of state trajectories, an appropriate notion of observability is presented which accommodates these phenomena. Based on this notion, we first derive a formula for the reconstruction of the state of the system where we explicitly obtain an injective mapping from the output to the state. In practice, such a mapping may be difficult to realize numerically and hence a class of estimators is proposed which ensures that the state estimate converges asymptotically to the real state of the system.},
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The problem of state reconstruction and estimation is considered for a class of switched dynamical systems whose subsystems are modeled using linear differential–algebraic equations (DAEs). Since this system class imposes time-varying dynamic and static (in the form of algebraic constraints) relations on the evolution of state trajectories, an appropriate notion of observability is presented which accommodates these phenomena. Based on this notion, we first derive a formula for the reconstruction of the state of the system where we explicitly obtain an injective mapping from the output to the state. In practice, such a mapping may be difficult to realize numerically and hence a class of estimators is proposed which ensures that the state estimate converges asymptotically to the real state of the system. |
Berger, Thomas; Reis, Timo; Trenn, Stephan Observability of linear differential-algebraic systems: A survey Book Section In: Ilchmann, Achim; Reis, Timo (Ed.): Surveys in Differential-Algebraic Equations IV, pp. 161–219, Springer-Verlag, Berlin-Heidelberg, 2017. @incollection{BergReis17,
title = {Observability of linear differential-algebraic systems: A survey},
author = {Thomas Berger and Timo Reis and Stephan Trenn},
editor = {Achim Ilchmann and Timo Reis},
url = {https://stephantrenn.net/wp-content/uploads/2017/09/Preprint-BRT150721.pdf, Preprint},
doi = {10.1007/978-3-319-46618-7_4},
year = {2017},
date = {2017-01-01},
booktitle = {Surveys in Differential-Algebraic Equations IV},
pages = {161--219},
publisher = {Springer-Verlag},
address = {Berlin-Heidelberg},
series = {Differential-Algebraic Equations Forum},
abstract = {We investigate different concepts related to observability of linear constant coefficient differential-algebraic equations. Regularity, which, loosely speaking, guarantees existence and uniqueness of solutions for any inhomogeneity, is not required in this article. Concepts like impulse observability, observability at infinity, behavioral observability, strong and complete observability are described and defined in the time-domain. Special emphasis is placed on a normal form under output injection, state space and output space transformation. This normal form together with duality is exploited to derive Hautus type criteria for observability. We also discuss geometric criteria, Kalman decompositions and detectability. Some new results on stabilization by output injection are proved.},
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We investigate different concepts related to observability of linear constant coefficient differential-algebraic equations. Regularity, which, loosely speaking, guarantees existence and uniqueness of solutions for any inhomogeneity, is not required in this article. Concepts like impulse observability, observability at infinity, behavioral observability, strong and complete observability are described and defined in the time-domain. Special emphasis is placed on a normal form under output injection, state space and output space transformation. This normal form together with duality is exploited to derive Hautus type criteria for observability. We also discuss geometric criteria, Kalman decompositions and detectability. Some new results on stabilization by output injection are proved. |
Küsters, Ferdinand; Trenn, Stephan; Wirsen, Andreas Observer design based on constant-input observability for DAEs Proceedings Article In: PAMM - Proc. Appl. Math. Mech., pp. 813–814, WILEY-VCH Verlag, 2016, ISSN: 1617-7061. @inproceedings{KustTren16b,
title = {Observer design based on constant-input observability for DAEs},
author = {Ferdinand Küsters and Stephan Trenn and Andreas Wirsen},
url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-KTW160511.pdf, Preprint},
doi = {10.1002/pamm.201610395},
issn = {1617-7061},
year = {2016},
date = {2016-01-01},
booktitle = {PAMM - Proc. Appl. Math. Mech.},
volume = {16},
number = {1},
pages = {813--814},
publisher = {WILEY-VCH Verlag},
abstract = {For differential-algebraic equations (DAEs) an observability notion is considered which assumes the input to be unknown and constant. Based on this, an observer design is proposed.},
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tppubtype = {inproceedings}
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For differential-algebraic equations (DAEs) an observability notion is considered which assumes the input to be unknown and constant. Based on this, an observer design is proposed. |
Tanwani, Aneel; Trenn, Stephan On detectability of switched linear differential-algebraic equations Proceedings Article In: Proc. 54th IEEE Conf. Decis. Control, Osaka, Japan, pp. 2957–2962, 2015. @inproceedings{TanwTren15,
title = {On detectability of switched linear differential-algebraic equations},
author = {Aneel Tanwani and Stephan Trenn},
url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-TT150904.pdf, Preprint},
doi = {10.1109/CDC.2015.7402666},
year = {2015},
date = {2015-12-03},
booktitle = {Proc. 54th IEEE Conf. Decis. Control, Osaka, Japan},
pages = {2957--2962},
abstract = {This paper addresses the notion of detectability for continuous-time switched systems comprising linear differential-algebraic equations (DAEs). It relates to studying asymptotic stability of the set of state trajectories corresponding to zero input and zero output, with a fixed switching signal. Due to the nature of solutions of switched DAEs, the problem reduces to analyzing stability of the trajectories emanating from a non-vanishing unobservable subspace, for which we first derive a geometric expression. The stability of state trajectories starting from that subspace can then be checked in two possible ways. In the first case, detectability of switched DAE is shown to be equivalent to the asymptotic stability of a reduced order discrete-time switched system. In the second approach, the solutions from a non-vanishing unobservable subspace are mapped to the solutions of a reduced order continuous system with time-varying switching ordinary differential equations (ODEs). As a special case of the later approach, the reduced order switched system is time-invariant if the unobservable subspace is invariant for all subsystems},
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This paper addresses the notion of detectability for continuous-time switched systems comprising linear differential-algebraic equations (DAEs). It relates to studying asymptotic stability of the set of state trajectories corresponding to zero input and zero output, with a fixed switching signal. Due to the nature of solutions of switched DAEs, the problem reduces to analyzing stability of the trajectories emanating from a non-vanishing unobservable subspace, for which we first derive a geometric expression. The stability of state trajectories starting from that subspace can then be checked in two possible ways. In the first case, detectability of switched DAE is shown to be equivalent to the asymptotic stability of a reduced order discrete-time switched system. In the second approach, the solutions from a non-vanishing unobservable subspace are mapped to the solutions of a reduced order continuous system with time-varying switching ordinary differential equations (ODEs). As a special case of the later approach, the reduced order switched system is time-invariant if the unobservable subspace is invariant for all subsystems |
Petreczky, Mihály; Tanwani, Aneel; Trenn, Stephan Observability of switched linear systems Book Section In: Djemai, Mohamed; Defoort, Michael (Ed.): Hybrid Dynamical Systems, vol. 457, pp. 205–240, 2015. @incollection{PetrTanw15,
title = {Observability of switched linear systems},
author = {Mihály Petreczky and Aneel Tanwani and Stephan Trenn},
editor = {Mohamed Djemai and Michael Defoort},
url = {https://stephantrenn.net/wp-content/uploads/2017/09/Preprint-PTT140211.pdf, Preprint},
doi = {10.1007/978-3-319-10795-0_8},
year = {2015},
date = {2015-01-01},
booktitle = {Hybrid Dynamical Systems},
volume = {457},
pages = {205--240},
abstract = {Observability of switched linear systems has been well studied during the past decade and depending on the notion of observability, several criteria have appeared in the literature. We will present these different approaches, with a focus on the recently introduced notion of large-time observability in the context of switched linear systems and its geometric characterization. These geometric conditions depend on computing the exponential of the matrix and require the exact knowledge of switching times, and it is shown that the proposed conditions have a denseness property with respect to switching times. To relieve the computation burden, some relaxed conditions that do not rely on the switching times are given; this allows for a direct comparison of the different observability notions. Furthermore, the generalization of the geometric approach to linear switched differential-algebraic systems is discussed. Detailed examples are included to illustrate the geometric conditions and to better understand the theoretical development.},
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Observability of switched linear systems has been well studied during the past decade and depending on the notion of observability, several criteria have appeared in the literature. We will present these different approaches, with a focus on the recently introduced notion of large-time observability in the context of switched linear systems and its geometric characterization. These geometric conditions depend on computing the exponential of the matrix and require the exact knowledge of switching times, and it is shown that the proposed conditions have a denseness property with respect to switching times. To relieve the computation burden, some relaxed conditions that do not rely on the switching times are given; this allows for a direct comparison of the different observability notions. Furthermore, the generalization of the geometric approach to linear switched differential-algebraic systems is discussed. Detailed examples are included to illustrate the geometric conditions and to better understand the theoretical development. |
