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:

Iervolino, Raffaele; Trenn, Stephan; Vasca, Francesco

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

IEEE Transactions on Automatic Control, 2021, (to appear).

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Wijnbergen, Paul; Jeeninga, Mark; Trenn, Stephan

On stabilizability of switched Differential Algebraic Equations Inproceedings

Proc. IFAC World Congress 2020, Berlin, Germany, 2020, (to appear).

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Hossain, Sumon; Trenn, Stephan

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

Proc. IFAC World Congress 2020, Berlin, Germany, 2020, (to appear).

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

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

Automatica, 2020, (to appear).

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Wijnbergen, Paul; Trenn, Stephan

Impulse controllability of switched differential-algebraic equations Inproceedings

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

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

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

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

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Chen, Yahao; Trenn, Stephan

On geometric and differentiation index of nonlinear differential-algebraic equations Unpublished

2020, (submitted for publication).

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Trenn, Stephan

The Laplace transform and inconsistent initial values Unpublished

2020, (extended abstract, submitted to MTNS).

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Iervolino, Raffaele; Vasca, Francesco; Trenn, Stephan

Discontinuous Lyapunov functions for discontinous piecewise-affine systems Unpublished

2020, (extended abstract, submitted to MTNS).

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Lee, Jin Gyu; Trenn, Stephan

Asymptotic tracking via funnel control Inproceedings

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

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Trenn, Stephan; Unger, Benjamin

Delay regularity of differential-algebraic equations Inproceedings

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

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

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

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

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Borsche, Raul; Kocoglu, Damla; Trenn, Stephan

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

2019, (submitted for publication).

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

Switch induced instabilities for stable power system DAE models Inproceedings

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

Abstract | Links | BibTeX