Trenn, Stephan Distributional restriction impossible to define Unpublished 2020, (submitted). @unpublished{Tren20ppf, title = {Distributional restriction impossible to define}, author = {Stephan Trenn}, url = {https://stephantrenn.net/wp-content/uploads/2020/09/Preprint-Tre200901.pdf, Preprint}, year = {2020}, date = {2020-09-01}, note = {submitted}, keywords = {}, pubstate = {published}, tppubtype = {unpublished} } |
Wijnbergen, Paul; Trenn, Stephan Impulse-free interval-stabilization of switched differential algebraic equations Unpublished 2020, (submitted). @unpublished{WijnTren20pp, title = {Impulse-free interval-stabilization of switched differential algebraic equations}, author = {Paul Wijnbergen and Stephan Trenn}, url = {https://stephantrenn.net/wp-content/uploads/2020/08/Preprint-WT200821.pdf, Preprint}, year = {2020}, date = {2020-08-21}, abstract = {In this paper stabilization of switched differential algebraic equations is considered, where Dirac impulses in both the input and the state trajectory are to be avoided during the stabilization process. First it is shown that stabilizability of a switched DAE and the existence of impulse-free solutions are merely necessary conditions for impulse-free stabilizability. Then necessary and sufficient conditions for the existence of impulse-free solutions are given, which motivate the definition of (impulse-free) interval-stabilization on a finite interval. Under a uniformity assumption, which can be verified for a broad class of switched systems, stabilizability on an infinite interval can be concluded based on interval-stabilizability. As a result a characterization of impulse-free interval stabilizability is given and as a corollary we provide a novel impulse-free null-controllability characterization. Finally, the results are compared to results on interval-stabilizability where Dirac impulses are allowed in the input and state trajectory. }, note = {submitted}, keywords = {}, pubstate = {published}, tppubtype = {unpublished} } In this paper stabilization of switched differential algebraic equations is considered, where Dirac impulses in both the input and the state trajectory are to be avoided during the stabilization process. First it is shown that stabilizability of a switched DAE and the existence of impulse-free solutions are merely necessary conditions for impulse-free stabilizability. Then necessary and sufficient conditions for the existence of impulse-free solutions are given, which motivate the definition of (impulse-free) interval-stabilization on a finite interval. Under a uniformity assumption, which can be verified for a broad class of switched systems, stabilizability on an infinite interval can be concluded based on interval-stabilizability. As a result a characterization of impulse-free interval stabilizability is given and as a corollary we provide a novel impulse-free null-controllability characterization. Finally, the results are compared to results on interval-stabilizability where Dirac impulses are allowed in the input and state trajectory. |
Borsche, Raul; Kocoglu, Damla; Trenn, Stephan A distributional solution framework for linear hyperbolic PDEs coupled to switched DAEs Unpublished 2020, (submitted for publication). @unpublished{BorsKoco20pp, title = {A distributional solution framework for linear hyperbolic PDEs coupled to switched DAEs}, author = {Raul Borsche and Damla Kocoglu and Stephan Trenn}, url = {https://stephantrenn.net/wp-content/uploads/2020/07/Preprint-BKT200707.pdf, Preprint https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5884, Preprint (on TU-KL server)}, year = {2020}, date = {2020-07-07}, abstract = {A distributional solution framework is developed for systems consisting of linear hyperbolic partial differential equations (PDEs) and switched differential-algebraic equations (DAEs) which are coupled via boundary conditions. The unique solvability is then characterize in terms of a switched delay DAE. The theory is illustrated with an example of electric power lines modeled by the telegraph equations which are coupled via a switching transformer where simulations confirm the predicted impulsive solutions.}, note = {submitted for publication}, keywords = {}, pubstate = {published}, tppubtype = {unpublished} } A distributional solution framework is developed for systems consisting of linear hyperbolic partial differential equations (PDEs) and switched differential-algebraic equations (DAEs) which are coupled via boundary conditions. The unique solvability is then characterize in terms of a switched delay DAE. The theory is illustrated with an example of electric power lines modeled by the telegraph equations which are coupled via a switching transformer where simulations confirm the predicted impulsive solutions. |
Lee, Jin Gyu; Trenn, Stephan; Shim, Hyungbo Synchronization with prescribed transient behavior: Heterogeneous multi-agent systems under funnel coupling Unpublished 2020, (submitted for publication). @unpublished{LeeTren20pp, title = {Synchronization with prescribed transient behavior: Heterogeneous multi-agent systems under funnel coupling}, author = {Jin Gyu Lee and Stephan Trenn and Hyungbo Shim}, url = {https://stephantrenn.net/wp-content/uploads/2020/07/Preprint-LTS200702.pdf, Preprint}, year = {2020}, date = {2020-07-02}, abstract = {In this paper, we introduce a nonlinear time-varying coupling law, which can be designed in a fully decentralized manner and achieves approximate synchronization with arbitrary precision, under only mild assumptions on the individual vector fields and the underlying graph structure. The proposed coupling law is motivated by the funnel control studied in adaptive controls under the observation that arbitrary precision synchronization can be achieved for heterogeneous multi-agent systems by the high-gain coupling, and thus, we follow to call our coupling law as `(node-wise) funnel coupling.' By getting out of the conventional proof technique in the funnel control study, we now can obtain even asymptotic or finite-time synchronization with the same funnel coupling law. More interestingly, the emergent collective behavior that arises for a heterogeneous multi-agent system when enforcing arbitrary precision synchronization by the proposed funnel coupling law, has been analyzed in this paper. In particular, we introduce a single scalar dynamics called `emergent dynamics' that is capable of illustrating the emergent synchronized behavior by its solution trajectory. Characterization of the emergent dynamics is important because, for instance, one can design the emergent dynamics first such that the solution trajectory behaves as desired, and then, provide a design guideline to each agent so that the constructed vector fields yield the desired emergent dynamics. A particular example illustrating the utility of the emergent dynamics is given also in the paper as a distributed median solver.}, note = {submitted for publication}, keywords = {}, pubstate = {published}, tppubtype = {unpublished} } In this paper, we introduce a nonlinear time-varying coupling law, which can be designed in a fully decentralized manner and achieves approximate synchronization with arbitrary precision, under only mild assumptions on the individual vector fields and the underlying graph structure. The proposed coupling law is motivated by the funnel control studied in adaptive controls under the observation that arbitrary precision synchronization can be achieved for heterogeneous multi-agent systems by the high-gain coupling, and thus, we follow to call our coupling law as `(node-wise) funnel coupling.' By getting out of the conventional proof technique in the funnel control study, we now can obtain even asymptotic or finite-time synchronization with the same funnel coupling law. More interestingly, the emergent collective behavior that arises for a heterogeneous multi-agent system when enforcing arbitrary precision synchronization by the proposed funnel coupling law, has been analyzed in this paper. In particular, we introduce a single scalar dynamics called `emergent dynamics' that is capable of illustrating the emergent synchronized behavior by its solution trajectory. Characterization of the emergent dynamics is important because, for instance, one can design the emergent dynamics first such that the solution trajectory behaves as desired, and then, provide a design guideline to each agent so that the constructed vector fields yield the desired emergent dynamics. A particular example illustrating the utility of the emergent dynamics is given also in the paper as a distributed median solver. |
Iervolino, Raffaele; Vasca, Francesco; Trenn, Stephan Discontinuous Lyapunov functions for discontinous piecewise-affine systems Unpublished 2020, (extended abstract, submitted to MTNS). @unpublished{IervTren20pp, title = {Discontinuous Lyapunov functions for discontinous piecewise-affine systems}, author = {Raffaele Iervolino and Francesco Vasca and Stephan Trenn}, url = {https://stephantrenn.net/wp-content/uploads/2020/01/Preprint-ITV200122.pdf, Preprint}, year = {2020}, date = {2020-01-22}, abstract = {Asymptotic stability of continuous-time piecewise affine systems defined over a polyhedral partition of the state space, with possible discontinuous vector field on the boundaries, is considered. We first introduce the feasible Filippov solution concept by characterizing single-mode Caratheodory, sliding mode and forward Zeno behaviors. Then, a global asymptotic stability result through a (possibly discontinuous) piecewise Lyapunov function is presented. The sufficient conditions are based on pointwise classifications of the trajectories which allow the identification of crossing, unreachable and Caratheodory boundaries. It is highlighted that the sign and jump conditions of the stability theorem can be expressed in terms of linear matrix inequalities by particularizing to piecewise quadratic Lyapunov functions and using the cone-copositivity approach. }, note = {extended abstract, submitted to MTNS}, keywords = {}, pubstate = {published}, tppubtype = {unpublished} } Asymptotic stability of continuous-time piecewise affine systems defined over a polyhedral partition of the state space, with possible discontinuous vector field on the boundaries, is considered. We first introduce the feasible Filippov solution concept by characterizing single-mode Caratheodory, sliding mode and forward Zeno behaviors. Then, a global asymptotic stability result through a (possibly discontinuous) piecewise Lyapunov function is presented. The sufficient conditions are based on pointwise classifications of the trajectories which allow the identification of crossing, unreachable and Caratheodory boundaries. It is highlighted that the sign and jump conditions of the stability theorem can be expressed in terms of linear matrix inequalities by particularizing to piecewise quadratic Lyapunov functions and using the cone-copositivity approach. |
Trenn, Stephan The Laplace transform and inconsistent initial values Unpublished 2020, (extended abstract, submitted to MTNS). @unpublished{Tren20b, title = {The Laplace transform and inconsistent initial values}, author = {Stephan Trenn}, url = {https://stephantrenn.net/wp-content/uploads/2020/01/Preprint-Tre200122.pdf, Preprint}, year = {2020}, date = {2020-01-22}, abstract = {Switches in electrical circuits may lead to Dirac impulses in the solution; a real word example utilizing this effect is the spark plug. Treating these Dirac impulses in a mathematically rigorous way is surprisingly challenging. This is in particular true for arguments made in the frequency domain in connection with the Laplace transform. A survey will be given on how inconsistent initials values have been treated in the past and how these approaches can be justified in view of the now available solution theory based on piecewise-smooth distributions.}, note = {extended abstract, submitted to MTNS}, keywords = {}, pubstate = {published}, tppubtype = {unpublished} } Switches in electrical circuits may lead to Dirac impulses in the solution; a real word example utilizing this effect is the spark plug. Treating these Dirac impulses in a mathematically rigorous way is surprisingly challenging. This is in particular true for arguments made in the frequency domain in connection with the Laplace transform. A survey will be given on how inconsistent initials values have been treated in the past and how these approaches can be justified in view of the now available solution theory based on piecewise-smooth distributions. |
Submitted
Distributional restriction impossible to define Unpublished 2020, (submitted). |
Impulse-free interval-stabilization of switched differential algebraic equations Unpublished 2020, (submitted). |
A distributional solution framework for linear hyperbolic PDEs coupled to switched DAEs Unpublished 2020, (submitted for publication). |
Synchronization with prescribed transient behavior: Heterogeneous multi-agent systems under funnel coupling Unpublished 2020, (submitted for publication). |
Discontinuous Lyapunov functions for discontinous piecewise-affine systems Unpublished 2020, (extended abstract, submitted to MTNS). |
The Laplace transform and inconsistent initial values Unpublished 2020, (extended abstract, submitted to MTNS). |