2024
|
Chang, Hamin; Song, Donghyeon; Trenn, Stephan; Shim, Hyungbo Disturbance observer with switched output redefinition for robust stabilization of non-minimum phase linear systems Proceedings Article In: Proc. 63rd IEEE Conf. Decision Control (CDC 2024), IEEE Milan, Italy, 2024, (to appear). @inproceedings{ChanSong24,
title = {Disturbance observer with switched output redefinition for robust stabilization of non-minimum phase linear systems},
author = {Hamin Chang and Donghyeon Song and Stephan Trenn and Hyungbo Shim},
url = {https://stephantrenn.net/wp-content/uploads/2024/09/Preprint-CSTS240909.pdf, Preprint},
year = {2024},
date = {2024-12-16},
urldate = {2024-12-16},
booktitle = {Proc. 63rd IEEE Conf. Decision Control (CDC 2024)},
address = {Milan, Italy},
organization = {IEEE},
abstract = {Q-filter-based disturbance observer (DOB) has emerged as a powerful robust control technique renowned for its effectiveness in mitigating disturbances and addressing plant uncertainties. Despite its advantage, a key limitation of the Q-filter-based DOB lies in its requirement for plants to be of minimum phase. In this paper, we introduce an approach allowing the utilization of the Q-filter-based DOB as a stabilizing controller for non-minimum phase linear systems based on switched output redefinition of the systems. By redefining the output of systems to be controlled periodically, the approach stabilizes unstable internal dynamics of the systems as well as the original output. The proposed method is verified by an illustrative example.},
note = {to appear},
keywords = {observer, relative-degree, switched-systems},
pubstate = {published},
tppubtype = {inproceedings}
}
Q-filter-based disturbance observer (DOB) has emerged as a powerful robust control technique renowned for its effectiveness in mitigating disturbances and addressing plant uncertainties. Despite its advantage, a key limitation of the Q-filter-based DOB lies in its requirement for plants to be of minimum phase. In this paper, we introduce an approach allowing the utilization of the Q-filter-based DOB as a stabilizing controller for non-minimum phase linear systems based on switched output redefinition of the systems. By redefining the output of systems to be controlled periodically, the approach stabilizes unstable internal dynamics of the systems as well as the original output. The proposed method is verified by an illustrative example. |
2023
|
Chang, Hamin; Trenn, Stephan Design of Q-filter-based disturbance observer for differential algebraic equations and a robust stability condition: Zero relative degree case Proceedings Article In: Proc. 62nd IEEE Conf. Decision Control, pp. 8489-8494, IEEE, 2023. @inproceedings{ChanTren23,
title = {Design of Q-filter-based disturbance observer for differential algebraic equations and a robust stability condition: Zero relative degree case},
author = {Hamin Chang and Stephan Trenn},
url = {https://stephantrenn.net/wp-content/uploads/2023/11/Preprint-CT230915.pdf, Preprint},
doi = {10.1109/CDC49753.2023.10383698},
year = {2023},
date = {2023-12-15},
urldate = {2023-12-15},
booktitle = {Proc. 62nd IEEE Conf. Decision Control},
pages = {8489-8494},
publisher = {IEEE},
abstract = {While the disturbance observer (DOB)-based controller is widely utilized in various practical applications, there has been a lack of extension of its use to differential algebraic equations (DAEs). In this paper, we introduce several lemmas that establish necessary and/or sufficient conditions for specifying the relative degree of DAEs. Using these lemmas, we also figure out that there is a class of DAEs which can be viewed as linear systems with zero relative degree. For the class of DAEs, we propose a design of Q-filter-based DOB as well as a robust stability condition for systems controlled by the DOB through time domain analysis using singular perturbation theory. The proposed stability condition is verified by an illustrative example.},
keywords = {DAEs, observer, relative-degree, stability},
pubstate = {published},
tppubtype = {inproceedings}
}
While the disturbance observer (DOB)-based controller is widely utilized in various practical applications, there has been a lack of extension of its use to differential algebraic equations (DAEs). In this paper, we introduce several lemmas that establish necessary and/or sufficient conditions for specifying the relative degree of DAEs. Using these lemmas, we also figure out that there is a class of DAEs which can be viewed as linear systems with zero relative degree. For the class of DAEs, we propose a design of Q-filter-based DOB as well as a robust stability condition for systems controlled by the DOB through time domain analysis using singular perturbation theory. The proposed stability condition is verified by an illustrative example. |
Yin, Hao; Jayawardhana, Bayu; Trenn, Stephan Contraction analysis of time-varying DAE systems via auxiliary ODE systems Unpublished 2023, (conditionally accepted at TAC). @unpublished{YinJaya23ppa,
title = {Contraction analysis of time-varying DAE systems via auxiliary ODE systems},
author = {Hao Yin and Bayu Jayawardhana and Stephan Trenn},
url = {https://stephantrenn.net/wp-content/uploads/2023/12/Preprint-YJT230920.pdf, Preprint},
year = {2023},
date = {2023-09-20},
urldate = {2023-09-20},
note = {conditionally accepted at TAC},
keywords = {DAEs, nonlinear, observer, stability},
pubstate = {published},
tppubtype = {unpublished}
}
|
2019
|
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.},
keywords = {DAEs, observability, observer, piecewise-smooth-distributions, switched-DAEs, switched-systems},
pubstate = {published},
tppubtype = {article}
}
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. |
2017
|
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.},
keywords = {observability, observer, switched-systems},
pubstate = {published},
tppubtype = {inproceedings}
}
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.},
keywords = {observability, observer, piecewise-smooth-distributions, switched-DAEs, switched-systems},
pubstate = {published},
tppubtype = {inproceedings}
}
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. |
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 = {DAEs, observability, observer, piecewise-smooth-distributions, stability, switched-DAEs, switched-systems},
pubstate = {published},
tppubtype = {inproceedings}
}
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.},
keywords = {DAEs, observability, observer, piecewise-smooth-distributions, switched-DAEs, switched-systems},
pubstate = {published},
tppubtype = {article}
}
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. |
2016
|
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.},
keywords = {DAEs, observability, observer},
pubstate = {published},
tppubtype = {inproceedings}
}
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. |
2013
|
Tanwani, Aneel; Trenn, Stephan An observer for switched differential-algebraic equations based on geometric characterization of observability Proceedings Article In: Proc. 52nd IEEE Conf. Decis. Control, Florence, Italy, pp. 5981–5986, 2013. @inproceedings{TanwTren13,
title = {An observer for switched differential-algebraic equations based on geometric characterization of observability},
author = {Aneel Tanwani and Stephan Trenn},
url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-TT130909.pdf, Preprint},
doi = {10.1109/CDC.2013.6760833},
year = {2013},
date = {2013-12-12},
booktitle = {Proc. 52nd IEEE Conf. Decis. Control, Florence, Italy},
pages = {5981--5986},
abstract = {Based on our previous work dealing with geometric characterization of observability for switched differential-algebraic equations (switched DAEs), we propose an observer design for switched DAEs that generates an asymptotically convergent state estimate. Without assuming the observability of individual modes, the central idea in constructing the observer is to filter out the maximal information from the output of each of the active subsystems and combine it with the previously extracted information to obtain a good estimate of the state after a certain time has passed. In general, observability only holds when impulses in the output are taken into account, hence our observer incorporates the knowledge of impulses in the output. This is a distinguishing feature of our observer design compared to observers for switched ordinary differential equations.},
keywords = {DAEs, observability, observer, piecewise-smooth-distributions, switched-DAEs, switched-systems},
pubstate = {published},
tppubtype = {inproceedings}
}
Based on our previous work dealing with geometric characterization of observability for switched differential-algebraic equations (switched DAEs), we propose an observer design for switched DAEs that generates an asymptotically convergent state estimate. Without assuming the observability of individual modes, the central idea in constructing the observer is to filter out the maximal information from the output of each of the active subsystems and combine it with the previously extracted information to obtain a good estimate of the state after a certain time has passed. In general, observability only holds when impulses in the output are taken into account, hence our observer incorporates the knowledge of impulses in the output. This is a distinguishing feature of our observer design compared to observers for switched ordinary differential equations. |
