was accepted for publication.
Furthermore, Yahao and I have finished a follow-up paper discussing the generalization of the consistency-projector to the nonlinear case:
In responds to invitations from Rafal Goebel and Tim Hughes/Malcom Smith I have submitted the following two extended abstracts to the MTNS 2020:
[Update 04-02-2020] My postdoc Yahao Chen was able to finish a nice result about the index of nonlinear DAEs just on time to submit it also to the MTNS (as a full paper):
[Update March 2021] Unfortunately the MTNS was cancelled, which means that the extended abstracts will not be published on the conference webpage (but I will keep them online under Miscellaneous). The full paper coauthored with Yahao Chen will be published in the proceedings.
Finally we have published our key theoretical paper four our DFG-project “Coupling hyperbolic PDEs with switched DAEs: Analysis, numerics and application to blood flow models”:
In this paper, we provide a novel distributional solution framework to handle jumps and Dirac impulses on the boundaries of the domain of a hyperbolic PDE. It also includes a nice example of electrical power lines (modeled via the telegraph equation) with a switching transformer (modeled by a switched DAE). The simulations nicely show how a Dirac impulse (induced by a switch) is moving through time and space as predicted by the theory.
Together with my PhD-students we have prepared the following two submission to the IFAC World Congress 2020 to be held in Berlin next year:
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.).
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.).
We have submitted the following two papers to the ECC’20 taking place in St. Petersburg, Russia:
In cooperation with colleagues from Seoul National University we have submitted the following paper
Already in our 2015 CDC paper
we proposed the idea of funnel synchronization and the simulations looked very promising, but at that time we were not able to prove the synchronization property and also were not able to characterize the emergent behavior. Jin Gyu Lee was able to find the right proof techniques which is now the corner stone of our new submission.
We have submitted the manuscript
My three Vietnames co-authors and I have analyzed the stability of switched linear singular system in discrete-time. The results build on our recently introduced notion of a one-step-map for index-1 switched singular systems:
We have submitted the following four papers to the CDC 2019 in Nice, France.
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.
Asymptotic tracking via funnel control Inproceedings
In: Proc. 58th IEEE Conf. Decision Control (CDC) 2019, pp. 4228-4233, Nice, France, 2019.
Delay regularity of differential-algebraic equations Inproceedings
In: Proc. 58th IEEE Conf. Decision Control (CDC) 2019, pp. 989-994, Nice, France, 2019.
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.
Finally, we have finished our paper
and submitted it for publication.
We have started to work on this topic almost four years ago when I visited Benevento. Inspired by the promising approach of using the cone-copositivity approach to find Lyapunov functions for piecewise-affine (PWA) systems in an automatic way, we were trying to extend this idea in two main directions: 1) We wanted to allow for discontinuous Lyapunov functions and 2) we wanted to cover also sliding and Zeno solutions. We obtained first results by focusing on the first point (i.e. we only considered classical solutions) and presented these ideas at the CDC 2017 in Melbourne, Australia. It turned out that the technicalities involved in dealing with general Filippov solutions were quite tricky and we still haven’t resolved all of them. In particular, we had to make two technical assumptions for PWA systems which we believe are always satisfied, because we could not construct counter examples which violates these assumptions, but we were also not able to prove them so far. Furthermore, classifying boundaries as crossing, non-reachable and sliding turned out to be harder as expected as well, in particular, due to the presence of Zeno-behavior. Nevertheless we have a very strong (i.e. not very conservative) Lyapunov stability theorem which is formulated in terms of pointwise-conditions. In order to use the cone-copositive approach it is necessary to make some uniformity assumption on the solution behavior along the boundaries, but these assumptions do not exclude Zeno and sliding behavior and allows discontinuities of the Lyapunov function on crossing boundaries.
We are now looking forward to receive constructive feedback from our peers to further improve on the manuscript for the final published version.
We have submitted the manuscript
for publication. The results of this manuscript are based on Tjorben’s PhD-thesis.