Analysis and Control of Switched Differential Algebraic Equations

Funding scheme/agency: VIDI, NWO
Budget: 800.000 EUR
Duration: 11/2017-10/2022

Summary: The combined presence of sudden structural changes and constrained dynamics in mathematical models of dynamical systems leads to non-existence of classical solutions. This problem occurs e.g. in models of power grids, electrical circuits, mutlibody systems or water distribution networks. Switched differential algebraic equations (switched DAEs) are a novel modeling framework for these dynamical systems. So far, switched DAEs are not used for modeling because neither a general solution theory nor control-theoretical methods are available. However, many systems need to be modeled as switched DAEs to capture essential effects like jumps or even Dirac impulses; the latter occur in reality e.g. in the form of sparks in electrical circuits or as water hammers in water networks.
In this VIDI project a distributional solution theory for nonlinear switched DAEs encompassing jumps and Dirac impulses will be developed. Based on the rigorous treatment of these impulsive effects, new diagnostic methods (e.g. observers and fault detectors) as well as new controller designs (in particular optimal controllers) will be derived. The distributional solution framework with its corresponding novel control theoretic approaches will not only be a mathematical breakthrough but will also have the potential to lead to sophisticated new methods to solve real world problems.
A special emphasis will be on analyzing models of the electrical power grid, which consist of the so called swing equations (ordinary differential equations) together with the power balance equations (nonlinear algebraic constraints). Faults or scheduled activation/deactivation of generators yield sudden structural changes of the power network (switches). The groundbreaking new diagnostic and control tools for switched DAEs will therefore have the potential to solve problems like the very pressing need to stabilize the power grid in the presence of an increasing number of renewable energy sources in order to prevent blackouts.

Full project proposal.

Researchers financed by the project:
– Stephan Trenn (PI, paid by project, 11/2017 – 10/2022)

Paul Wijnbergen (PhD, paid by project, 08/2018-07/2022)

Yahao Chen (Postdoc, paid by project, 09/2019-08/2021)

Researchers involved in project without being financed by it

Anh, Pham Ky; Berger, Thomas; Borsche, Raul; Gross, Tjorben; Hossain, Sumon; Iervolino, Raffaele; Jeeninga, Mark; Kocoglu, Damla; Lee, Jin Gyu; Linh, Pham Thi; Shim, Hyungbo; Thuan, Do DucUnger, Benjamin; Vasca, FrancescoWirsen, Andreas

Research results obtained during the project:

Hossain, Sumon; Trenn, Stephan

Reduced realization of switched linear systems with known switching sequence Unpublished

2021, (submitted).

Abstract | Links | BibTeX

Lee, Jin Gyu; Berger, Thomas; Trenn, Stephan; Shim, Hyungbo

Edge-wise funnel output synchronization of heterogeneous agents with relative degree one Unpublished

2021, (submitted).

Abstract | Links | BibTeX

Berger, Thomas; Ilchmann, Achim; Trenn, Stephan

Quasi feedback forms for differential-algebraic systems Journal Article

In: IMA Journal of Mathematical Control and Information, (dnab030), pp. 1-31, 2021, (to appear).

Abstract | Links | BibTeX

Wijnbergen, Paul; Trenn, Stephan

Optimal control of DAEs with unconstrained terminal costs Inproceedings

In: Proc. 60th IEEE Conf. Decision and Control (CDC 2021), 2021, (to appear).

Abstract | Links | BibTeX

Hossain, Sumon; Trenn, Stephan

Minimal realization for linear switched systems with a single switch Inproceedings

In: Proc. European Control Conference (ECC21), Rotterdam, Netherlands, 2021, (to appear).

Abstract | Links | BibTeX

Chen, Yahao; Trenn, Stephan

Impulse-free jump solutions of nonlinear differential-algebraic equations Unpublished

2021, (submitted).

Abstract | Links | BibTeX

Chen, Yahao; Trenn, Stephan

On geometric and differentiation index of nonlinear differential-algebraic equations Inproceedings

In: Proceedings of the MTNS 2020/21, 2021, (to appear).

Abstract | Links | BibTeX

Iervolino, Raffaele; Trenn, Stephan; Vasca, Francesco

Asymptotic stability of piecewise affine systems with Filippov solutions via discontinuous piecewise Lyapunov functions Journal Article

In: IEEE Transactions on Automatic Control, 66 (4), pp. 1513-1528, 2021.

Abstract | Links | BibTeX

Trenn, Stephan; Unger, Benjamin

Unimodular transformations for DAE initial trajectory problems Inproceedings

In: PAMM · Proc. Appl. Math. Mech., pp. e202000322, Wiley-VCH GmbH, 2021, (Open Access.).

Abstract | Links | BibTeX

Chen, Yahao; Trenn, Stephan

The differentiation index of nonlinear differential-algebraic equations versus the relative degree of nonlinear control systems Inproceedings

In: PAMM · Proc. Appl. Math. Mech. 2020, pp. e202000162, Wiley-VCH GmbH, 2021, (Open Access.).

Abstract | Links | BibTeX

Wijnbergen, Paul; Trenn, Stephan

Impulse-free interval-stabilization of switched differential algebraic equations Journal Article

In: Systems & Control Letters, 149 , pp. 104870.1-10, 2021, (Open Access.).

Abstract | Links | BibTeX

Borsche, Raul; Kocoglu, Damla; Trenn, Stephan

A distributional solution framework for linear hyperbolic PDEs coupled to switched DAEs Journal Article

In: Mathematics of Control, Signals, and Systems (MCSS), 32 , pp. 455-487, 2020, (Open Access).

Abstract | Links | BibTeX

Anh, Pham Ky; Linh, Pham Thi; Thuan, Do Duc; Trenn, Stephan

Stability analysis for switched discrete-time linear singular systems Journal Article

In: Automatica, 119 (109100), 2020.

Abstract | Links | BibTeX

Wijnbergen, Paul; Jeeninga, Mark; Trenn, Stephan

On stabilizability of switched differential algebraic equations Inproceedings

In: IFAC-PapersOnLine 53-2, pp. 4304-4309, 2020, (Proc. IFAC World Congress 2020, Berlin, Germany. Open access.).

Abstract | Links | BibTeX

Hossain, Sumon; Trenn, Stephan

A time-varying Gramian based model reduction approach for Linear Switched Systems Inproceedings

In: IFAC PapersOnline 53-2, pp. 5629-5634, 2020, (Proc. IFAC World Congress 2020, Berlin, Germany. Open access.).

Abstract | Links | BibTeX

Wijnbergen, Paul; Trenn, Stephan

Impulse controllability of switched differential-algebraic equations Inproceedings

In: Proc. European Control Conference (ECC 2020), pp. 1561-1566, Saint Petersburg, Russia, 2020.

Abstract | Links | BibTeX

Lee, Jin Gyu; Berger, Thomas; Trenn, Stephan; Shim, Hyungbo

Utility of edge-wise funnel coupling for asymptotically solving distributed consensus optimization Inproceedings

In: Proc. European Control Conference (ECC 2020), pp. 911-916, Saint Petersburg, Russia, 2020.

Abstract | Links | BibTeX

Wijnbergen, Paul; Trenn, Stephan

A forward approach to controllability of switched DAEs Miscellaneous

Book of Abstracts - 39th Benelux Meeting on Systems and Control, 2020.

Links | BibTeX

Hossain, Sumon; Trenn, Stephan

Model reduction of switched systems in time-varying approach Miscellaneous

Book of Abstracts - 39th Benelux Meeting on Systems and Control, 2020.

Links | BibTeX

Trenn, Stephan

The Laplace transform and inconsistent initial values Miscellaneous

Extended Abstract, 2020, (accepted for cancelled MTNS 20/21).

Abstract | Links | BibTeX

Iervolino, Raffaele; Vasca, Francesco; Trenn, Stephan

Discontinuous Lyapunov functions for discontinous piecewise-affine systems Miscellaneous

Extended Abstract, 2020, (accepted for cancelled MTNS 20/21).

Abstract | Links | BibTeX

Lee, Jin Gyu; Trenn, Stephan

Asymptotic tracking via funnel control Inproceedings

In: Proc. 58th IEEE Conf. Decision Control (CDC) 2019, pp. 4228-4233, Nice, France, 2019.

Abstract | Links | BibTeX

Trenn, Stephan; Unger, Benjamin

Delay regularity of differential-algebraic equations Inproceedings

In: Proc. 58th IEEE Conf. Decision Control (CDC) 2019, pp. 989-994, Nice, France, 2019.

Abstract | Links | BibTeX

Anh, Pham Ky; Linh, Pham Thi; Thuan, Do Duc; Trenn, Stephan

The one-step-map for switched singular systems in discrete-time Inproceedings

In: Proc. 58th IEEE Conf. Decision Control (CDC) 2019, pp. 605-610, Nice, France, 2019.

Abstract | Links | BibTeX

Trenn, Stephan

Asymptotic tracking with funnel control Inproceedings

In: PAMM - Proc. Appl. Math. Mech., WILEY-VCH Verlag, 2019, (online).

Abstract | Links | BibTeX

Patil, Deepak; Tesi, Pietro; Trenn, Stephan

Indiscernible topological variations in DAE networks Journal Article

In: Automatica, 101 , pp. 280-289, 2019.

Abstract | Links | BibTeX

Tanwani, Aneel; Trenn, Stephan

Detectability and observer design for switched differential algebraic equations Journal Article

In: Automatica, 99 , pp. 289-300, 2019.

Abstract | Links | BibTeX

Gross, Tjorben B.; Trenn, Stephan; Wirsen, Andreas

Switch induced instabilities for stable power system DAE models Inproceedings

In: IFAC-PapersOnLine, pp. 127-132, 2018, (Proc. IFAC Conf. Analysis Design Hybrid Systems (ADHS 2018)).

Abstract | Links | BibTeX