2022
|
Mostacciuolo, Elisa; Trenn, Stephan; Vasca, Francesco Averaging for switched impulsive systems with pulse width modulation Unpublished 2022, (submitted). @unpublished{MostTren22ppb,
title = {Averaging for switched impulsive systems with pulse width modulation},
author = {Elisa Mostacciuolo and Stephan Trenn and Francesco Vasca},
url = {https://stephantrenn.net/wp-content/uploads/2022/11/Preprint-MTV221128.pdf, Preprint},
year = {2022},
date = {2022-11-28},
urldate = {2022-11-28},
abstract = {Linear switched impulsive systems (SIS) are characterized by ordinary differential equations as modes dynamics and state jumps at the switching time instants. The presence of possible jumps in the state makes nontrivial the application of classical averaging techniques. In this paper we consider SIS with pulse width modulation (PWM) and we propose an averaged model whose solution approximates the moving average of the SIS solution with an error which decreases with the multiple of the switching period and by decreasing the PWM period. The averaging result requires milder assumptions on the system matrices with respect to those needed by the previous averaging techniques for SIS. The interest of the proposed model is strengthened by the fact that it reduces to the classical averaged model for PWM systems when there are no jumps in the state. The theoretical results are verified through numerical results obtained by considering a switched capacitor electrical circuit.},
note = {submitted},
keywords = {application, averaging, DAEs, LMIs, switched-DAEs, switched-systems},
pubstate = {published},
tppubtype = {unpublished}
}
Linear switched impulsive systems (SIS) are characterized by ordinary differential equations as modes dynamics and state jumps at the switching time instants. The presence of possible jumps in the state makes nontrivial the application of classical averaging techniques. In this paper we consider SIS with pulse width modulation (PWM) and we propose an averaged model whose solution approximates the moving average of the SIS solution with an error which decreases with the multiple of the switching period and by decreasing the PWM period. The averaging result requires milder assumptions on the system matrices with respect to those needed by the previous averaging techniques for SIS. The interest of the proposed model is strengthened by the fact that it reduces to the classical averaged model for PWM systems when there are no jumps in the state. The theoretical results are verified through numerical results obtained by considering a switched capacitor electrical circuit. |
Mostacciuolo, Elisa; Trenn, Stephan; Vasca, Francesco An averaged model for switched systems with state jumps applicable for PWM descriptor systems Proceedings Article In: Proceedings of the 2022 European Control Conference (ECC), pp. 1085-1090, London, 2022. @inproceedings{MostTren22b,
title = {An averaged model for switched systems with state jumps applicable for PWM descriptor systems},
author = {Elisa Mostacciuolo and Stephan Trenn and Francesco Vasca},
url = {https://stephantrenn.net/wp-content/uploads/2022/03/Preprint-MTV220329.pdf, Preprint},
doi = {10.23919/ECC55457.2022.9838189},
year = {2022},
date = {2022-07-12},
urldate = {2022-07-12},
booktitle = {Proceedings of the 2022 European Control Conference (ECC)},
pages = {1085-1090},
address = {London},
abstract = {Switched descriptor systems with pulse width modulation are characterized by modes whose dynamics are described by differential algebraic equations; this type of models can be viewed as switched impulsive systems, i.e. switched systems with ordinary differential equations as modes dynamics and state jumps at the switching time instants. The presence of possible jumps in the state makes the application of the classical averaging technique nontrivial. In this paper we propose an averaged model for switched impulsive systems. The state trajectory of the proposed averaged model is shown to approximate the one of the original system with an error of order of the switching period. The model reduces to the classical averaged model when there are no jumps in the state. The practical interest of the theoretical averaging result is demonstrated through numerical simulations of a switched capacitor electrical circuit.},
keywords = {averaging, DAEs, switched-DAEs, switched-systems},
pubstate = {published},
tppubtype = {inproceedings}
}
Switched descriptor systems with pulse width modulation are characterized by modes whose dynamics are described by differential algebraic equations; this type of models can be viewed as switched impulsive systems, i.e. switched systems with ordinary differential equations as modes dynamics and state jumps at the switching time instants. The presence of possible jumps in the state makes the application of the classical averaging technique nontrivial. In this paper we propose an averaged model for switched impulsive systems. The state trajectory of the proposed averaged model is shown to approximate the one of the original system with an error of order of the switching period. The model reduces to the classical averaged model when there are no jumps in the state. The practical interest of the theoretical averaging result is demonstrated through numerical simulations of a switched capacitor electrical circuit. |
Mostacciuolo, Elisa; Trenn, Stephan; Vasca, Francesco A smooth model for periodically switched descriptor systems Journal Article In: Automatica, vol. 136, no. 110082, pp. 1-8, 2022, (open access). @article{MostTren22,
title = {A smooth model for periodically switched descriptor systems},
author = {Elisa Mostacciuolo and Stephan Trenn and Francesco Vasca},
url = {https://stephantrenn.net/wp-content/uploads/2021/04/Preprint-MTV210921.pdf, Preprint},
doi = {10.1016/j.automatica.2021.110082},
year = {2022},
date = {2022-02-01},
urldate = {2021-09-21},
journal = {Automatica},
volume = {136},
number = {110082},
pages = {1-8},
abstract = {Switched descriptor systems characterized by a repetitive finite sequence of modes can exhibit state discontinuities at the switching time instants. The amplitudes of these discontinuities depend on the consistency projectors of the modes. A switched ordinary differential equations model whose continuous state evolution approximates the state of the original system is proposed. Sufficient conditions based on linear matrix inequalities on the modes projectors ensure that the approximation error is of linear order of the switching period. The theoretical findings are applied to a switched capacitor circuit and numerical results illustrate the practical usefulness of the proposed model.},
note = {open access},
keywords = {averaging, DAEs, open-access, switched-DAEs, switched-systems},
pubstate = {published},
tppubtype = {article}
}
Switched descriptor systems characterized by a repetitive finite sequence of modes can exhibit state discontinuities at the switching time instants. The amplitudes of these discontinuities depend on the consistency projectors of the modes. A switched ordinary differential equations model whose continuous state evolution approximates the state of the original system is proposed. Sufficient conditions based on linear matrix inequalities on the modes projectors ensure that the approximation error is of linear order of the switching period. The theoretical findings are applied to a switched capacitor circuit and numerical results illustrate the practical usefulness of the proposed model. |
2017
|
Mostacciuolo, Elisa; Trenn, Stephan; Vasca, Francesco Averaging for switched DAEs: convergence, partial averaging and stability Journal Article In: Automatica, vol. 82, pp. 145–157, 2017. @article{MostTren17,
title = {Averaging for switched DAEs: convergence, partial averaging and stability},
author = {Elisa Mostacciuolo and Stephan Trenn and Francesco Vasca},
url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-MTV170407.pdf, Preprint},
doi = {10.1016/j.automatica.2017.04.036},
year = {2017},
date = {2017-08-01},
journal = {Automatica},
volume = {82},
pages = {145--157},
abstract = {Averaging is a useful technique to simplify the analysis of switched systems. In this paper we present averaging results for the class of systems described by switched differential algebraic equations (DAEs). Conditions on the consistency projectors are given which guarantee convergence towards a non-switched averaged system. A consequence of this result is the possibility to stabilize switched DAEs via fast switching. We also study partial averaging in case the consistency projectors do not satisfy the conditions for convergence; the averaged system is then still a switched system, but is simpler than the original. The practical interest of the theoretical averaging results is demonstrated through the analysis of the dynamics of a switched electrical circuit.},
keywords = {averaging, DAEs, stability, switched-DAEs, switched-systems},
pubstate = {published},
tppubtype = {article}
}
Averaging is a useful technique to simplify the analysis of switched systems. In this paper we present averaging results for the class of systems described by switched differential algebraic equations (DAEs). Conditions on the consistency projectors are given which guarantee convergence towards a non-switched averaged system. A consequence of this result is the possibility to stabilize switched DAEs via fast switching. We also study partial averaging in case the consistency projectors do not satisfy the conditions for convergence; the averaged system is then still a switched system, but is simpler than the original. The practical interest of the theoretical averaging results is demonstrated through the analysis of the dynamics of a switched electrical circuit. |
2016
|
Trenn, Stephan Stabilization of switched DAEs via fast switching Proceedings Article In: PAMM - Proc. Appl. Math. Mech., pp. 827–828, WILEY-VCH Verlag, 2016, ISSN: 1617-7061. @inproceedings{Tren16,
title = {Stabilization of switched DAEs via fast switching},
author = {Stephan Trenn},
url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-Tre160511.pdf, Preprint},
doi = {10.1002/pamm.201610402},
issn = {1617-7061},
year = {2016},
date = {2016-05-12},
booktitle = {PAMM - Proc. Appl. Math. Mech.},
volume = {16},
number = {1},
pages = {827--828},
publisher = {WILEY-VCH Verlag},
abstract = {Switched differential algebraic equations (switched DAEs) can model dynamical systems with state constraints together with sudden structural changes (switches). These switches may lead to induced jumps and can destabilize the system even in the case that each mode is stable. However, the opposite effect is also possible; in particular, the question of finding a stabilizing switching signal is of interest. Two approaches are presented how to stabilize a switched DAE via fast switching.},
keywords = {averaging, DAEs, stability, switched-DAEs, switched-systems},
pubstate = {published},
tppubtype = {inproceedings}
}
Switched differential algebraic equations (switched DAEs) can model dynamical systems with state constraints together with sudden structural changes (switches). These switches may lead to induced jumps and can destabilize the system even in the case that each mode is stable. However, the opposite effect is also possible; in particular, the question of finding a stabilizing switching signal is of interest. Two approaches are presented how to stabilize a switched DAE via fast switching. |
2015
|
Trenn, Stephan Distributional averaging of switched DAEs with two modes Proceedings Article In: Proc. 54th IEEE Conf. Decis. Control, Osaka, Japan, pp. 3616–3620, 2015. @inproceedings{Tren15,
title = {Distributional averaging of switched DAEs with two modes},
author = {Stephan Trenn},
url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-Tre150812.pdf, Preprint},
doi = {10.1109/CDC.2015.7402779},
year = {2015},
date = {2015-12-04},
booktitle = {Proc. 54th IEEE Conf. Decis. Control, Osaka, Japan},
pages = {3616--3620},
abstract = {The averaging technique is a powerful tool for the analysis and control of switched systems. Recently, classical averaging results were generalized to the class of switched differential algebraic equations (switched DAEs). These results did not consider the possible Dirac impulses in the solutions of switched DAEs and it was believed that the presence of Dirac impulses does not prevent convergence towards an average model and can therefore be neglected. It turns out that the first claim (convergence) is indeed true, but nevertheless the Dirac impulses cannot be neglected, they play an important role for the resulting limit. This note first shows with a simple example how the presence of Dirac impulses effects the convergence towards an averaged model and then a formal proof of convergence in the distributional sense for switched DAEs with two modes is given.},
keywords = {averaging, CDC, DAEs, piecewise-smooth-distributions, switched-DAEs, switched-systems},
pubstate = {published},
tppubtype = {inproceedings}
}
The averaging technique is a powerful tool for the analysis and control of switched systems. Recently, classical averaging results were generalized to the class of switched differential algebraic equations (switched DAEs). These results did not consider the possible Dirac impulses in the solutions of switched DAEs and it was believed that the presence of Dirac impulses does not prevent convergence towards an average model and can therefore be neglected. It turns out that the first claim (convergence) is indeed true, but nevertheless the Dirac impulses cannot be neglected, they play an important role for the resulting limit. This note first shows with a simple example how the presence of Dirac impulses effects the convergence towards an averaged model and then a formal proof of convergence in the distributional sense for switched DAEs with two modes is given. |
Mostacciuolo, Elisa; Trenn, Stephan; Vasca, Francesco Averaging for non-homogeneous switched DAEs Proceedings Article In: Proc. 54th IEEE Conf. Decis. Control, Osaka, Japan, pp. 2951–2956, 2015. @inproceedings{MostTren15b,
title = {Averaging for non-homogeneous switched DAEs},
author = {Elisa Mostacciuolo and Stephan Trenn and Francesco Vasca},
url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-MTV150901.pdf, Preprint},
doi = {10.1109/CDC.2015.7402665},
year = {2015},
date = {2015-12-02},
booktitle = {Proc. 54th IEEE Conf. Decis. Control, Osaka, Japan},
pages = {2951--2956},
abstract = {Averaging is widely used for approximating the dynamics of switched systems. The validity of an averaged model typically depends on the switching frequency and on some technicalities regarding the switched system structure. For homogeneous linear switched differential algebraic equations it is known that an averaged model can be obtained. In this paper an averaging result for non-homogeneous switched systems is presented. A switched electrical circuit illustrates the practical interest of the result.},
keywords = {application, averaging, CDC, DAEs, switched-DAEs, switched-systems},
pubstate = {published},
tppubtype = {inproceedings}
}
Averaging is widely used for approximating the dynamics of switched systems. The validity of an averaged model typically depends on the switching frequency and on some technicalities regarding the switched system structure. For homogeneous linear switched differential algebraic equations it is known that an averaged model can be obtained. In this paper an averaging result for non-homogeneous switched systems is presented. A switched electrical circuit illustrates the practical interest of the result. |
Mostacciuolo, Elisa; Trenn, Stephan; Vasca, Francesco Partial averaging for switched DAEs with two modes Proceedings Article In: Proc. 2015 European Control Conf. (ECC), Linz, Austria, pp. 2896–2901, 2015. @inproceedings{MostTren15a,
title = {Partial averaging for switched DAEs with two modes},
author = {Elisa Mostacciuolo and Stephan Trenn and Francesco Vasca},
url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-MTV150316.pdf, Preprint},
doi = {10.1109/ECC.2015.7330977},
year = {2015},
date = {2015-03-01},
booktitle = {Proc. 2015 European Control Conf. (ECC), Linz, Austria},
pages = {2896--2901},
abstract = {In this paper an averaging result for switched systems whose modes are represented by means of differential algebraic equations (DAEs) is presented. Homogeneous switched DAEs with periodic switchings between two modes are considered. It is proved that a (switched) averaged system can be defined also in the presence of state jumps whose amplitude does not decrease with the increasing of the switching frequency. A switched capacitor electrical circuit is considered as an illustrative example.},
keywords = {averaging, DAEs, switched-DAEs, switched-systems},
pubstate = {published},
tppubtype = {inproceedings}
}
In this paper an averaging result for switched systems whose modes are represented by means of differential algebraic equations (DAEs) is presented. Homogeneous switched DAEs with periodic switchings between two modes are considered. It is proved that a (switched) averaged system can be defined also in the presence of state jumps whose amplitude does not decrease with the increasing of the switching frequency. A switched capacitor electrical circuit is considered as an illustrative example. |
2013
|
Iannelli, Luigi; Pedicini, Carmen; Trenn, Stephan; Vasca, Francesco An averaging result for switched DAEs with multiple modes Proceedings Article In: Proc. 52nd IEEE Conf. Decis. Control, Florence, Italy, pp. 1378 - 1383, 2013. @inproceedings{IannPedi13b,
title = {An averaging result for switched DAEs with multiple modes},
author = {Luigi Iannelli and Carmen Pedicini and Stephan Trenn and Francesco Vasca},
url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-IPTV130911.pdf, Preprint},
doi = {10.1109/CDC.2013.6760075},
year = {2013},
date = {2013-12-10},
booktitle = {Proc. 52nd IEEE Conf. Decis. Control, Florence, Italy},
pages = {1378 - 1383},
abstract = {The major motivation of the averaging technique for switched systems is the construction of a smooth average system whose state trajectory approximates in some sense the state trajectory of the switched system. Averaging of dynamic systems represented by switched ordinary differential equations (ODEs) has been widely analyzed in the literature. The averaging approach can be useful also for the analysis of switched differential algebraic equations (DAEs). Indeed by analyzing the evolution of the switched DAEs state it is possible to conjecture the existence of an average model. However a trivial generalization of the ODE case is not possible due to the presence of state jumps. In this paper we discuss the averaging approach for switched DAEs and an approximation result is derived for homogenous switched linear DAE with periodic switching signals commuting among several modes. This approximation result extends a recent averaging result for switched DAEs with only two modes. Numerical simulations confirm the validity of the averaging approach for switched DAEs.},
keywords = {averaging, CDC, DAEs, switched-DAEs, switched-systems},
pubstate = {published},
tppubtype = {inproceedings}
}
The major motivation of the averaging technique for switched systems is the construction of a smooth average system whose state trajectory approximates in some sense the state trajectory of the switched system. Averaging of dynamic systems represented by switched ordinary differential equations (ODEs) has been widely analyzed in the literature. The averaging approach can be useful also for the analysis of switched differential algebraic equations (DAEs). Indeed by analyzing the evolution of the switched DAEs state it is possible to conjecture the existence of an average model. However a trivial generalization of the ODE case is not possible due to the presence of state jumps. In this paper we discuss the averaging approach for switched DAEs and an approximation result is derived for homogenous switched linear DAE with periodic switching signals commuting among several modes. This approximation result extends a recent averaging result for switched DAEs with only two modes. Numerical simulations confirm the validity of the averaging approach for switched DAEs. |
Iannelli, Luigi; Pedicini, Carmen; Trenn, Stephan; Vasca, Francesco Averaging for switched DAEs Proceedings Article In: PAMM - Proc. Appl. Math. Mech., pp. 489–490, WILEY-VCH Verlag, 2013, ISSN: 1617-7061. @inproceedings{IannPedi13c,
title = {Averaging for switched DAEs},
author = {Luigi Iannelli and Carmen Pedicini and Stephan Trenn and Francesco Vasca},
url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-IPTV130527.pdf, Preprint},
doi = {10.1002/pamm.201310237},
issn = {1617-7061},
year = {2013},
date = {2013-10-01},
booktitle = {PAMM - Proc. Appl. Math. Mech.},
volume = {13},
number = {1},
pages = {489--490},
publisher = {WILEY-VCH Verlag},
abstract = {Switched differential-algebraic equations (switched DAEs) E_sigma(t) x'(t) = A_sigma(t) x(t) are suitable for modeling many practical systems, e.g. electrical circuits. When the switching is periodic and of high frequency, the question arises whether the solutions of switched DAEs can be approximated by an average non-switching system. It is well known that for a quite general class of switched ordinary differential equations (ODEs) this is the case. For switched DAEs, due the presence of the so-called consistency projectors, it is possible that the limit of trajectories for faster and faster switching does not exist. Under certain assumptions on the consistency projectors a result concerning the averaging for switched DAEs is presented.},
keywords = {averaging, DAEs, switched-DAEs, switched-systems},
pubstate = {published},
tppubtype = {inproceedings}
}
Switched differential-algebraic equations (switched DAEs) E_sigma(t) x'(t) = A_sigma(t) x(t) are suitable for modeling many practical systems, e.g. electrical circuits. When the switching is periodic and of high frequency, the question arises whether the solutions of switched DAEs can be approximated by an average non-switching system. It is well known that for a quite general class of switched ordinary differential equations (ODEs) this is the case. For switched DAEs, due the presence of the so-called consistency projectors, it is possible that the limit of trajectories for faster and faster switching does not exist. Under certain assumptions on the consistency projectors a result concerning the averaging for switched DAEs is presented. |
Iannelli, Luigi; Pedicini, Carmen; Trenn, Stephan; Vasca, Francesco On averaging for switched linear differential algebraic equations Proceedings Article In: Proc. 12th European Control Conf. (ECC) 2013, Zurich, Switzerland, pp. 2163 – 2168, 2013. @inproceedings{IannPedi13a,
title = {On averaging for switched linear differential algebraic equations},
author = {Luigi Iannelli and Carmen Pedicini and Stephan Trenn and Francesco Vasca},
url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-IPTV130326.pdf, Preprint
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6669240, IEEE Xplore Article Number 6669240},
year = {2013},
date = {2013-07-02},
booktitle = {Proc. 12th European Control Conf. (ECC) 2013, Zurich, Switzerland},
pages = {2163 -- 2168},
abstract = {Averaging is an effective technique which allows the analysis and control design of nonsmooth switched systems through the use of corresponding simpler smooth averaged systems. Approximation results and stability analysis have been presented in the literature for dynamic systems described by switched ordinary differential equations. In this paper the averaging technique is shown to be useful also for the analysis of switched systems whose modes are represented by means of differential algebraic equations (DAEs). An approximation result is derived for a simple but representative homogenous switched DAE with periodic switching signals and two modes. Simulations based on a simple electric circuit model illustrate the theoretical result.},
keywords = {averaging, DAEs, switched-DAEs, switched-systems},
pubstate = {published},
tppubtype = {inproceedings}
}
Averaging is an effective technique which allows the analysis and control design of nonsmooth switched systems through the use of corresponding simpler smooth averaged systems. Approximation results and stability analysis have been presented in the literature for dynamic systems described by switched ordinary differential equations. In this paper the averaging technique is shown to be useful also for the analysis of switched systems whose modes are represented by means of differential algebraic equations (DAEs). An approximation result is derived for a simple but representative homogenous switched DAE with periodic switching signals and two modes. Simulations based on a simple electric circuit model illustrate the theoretical result. |
