Title: Dynamical boundary conditions for the water hammer problem.
Abstract: We are using hyperbolic balanced laws to model the fluid flow in the water pipes, and specifically the partial differential equation (PDE) used is a 1d Euler system with a semi-linear friction term. This coupled system in divergence form with semi-linearity is otherwise known as the isothermal Euler or Saint-Venant equations with friction. In [1] a switched differential algebraic equation (sDAE) model is used to approximate the water hammer model, however the approximation accuracy has not been investigated there. Therefore, the goal of this article is to show that a class of the solutions of the sDAE model for the water hammer problem converges to a nonlinear PDE solution under some stringent assumptions on the water density.
[1] R. Kausar and S. Trenn, Water hammer modeling for water networks via hyperbolic PDEs and switched DAEs, 2018.
The colloquium will take place online in Google Meet. You can email the organizer for a link to the meeting.
Title: Kernel-based models for system analysis
Abstract: This talk introduces a computational framework to identify nonlinear input-output operators from data. The goal is to find operators that fit a set of system trajectories while satisfying prior knowledge in the form of integral quadratic constraints. The data fitting algorithm is thus regularized by suitable input-output properties required for system analysis and control design. This biased identification problem is shown to admit the tractable solution of a regularized least squares problem when formulated in a suitable reproducing kernel Hilbert space. The kernel-based framework is a departure from the prevailing state-space framework. It is motivated by fundamental limitations of nonlinear state-space models at combining the fitting requirements of data-based modeling with the input-output requirements of system analysis and physical modeling.
The colloquium will take place online in Google Meet. You can email the organizer for a link to the meeting.
Title: On internal and external notions of string stability
Abstract: String stability is an important concept in the analysis and control of vehicle platoons (“strings”) as it prohibits the amplification of disturbances through the string. However, various – somewhat scattered – notions of string stability exist in the literature, ranging from stability-like properties of an equilibrium (internal) to performance-like properties (external). In this talk I will discuss some very preliminary ideas for linking such internal and external string stability properties by drawing inspiration from dissipativity theory.
The colloquium will take place online in Google Meet. You can email the organizer for a link to the meeting.
Dr. Henk van Waarde has joined the SCO group as Assistant Professor for Data-driven control in January 2022. Henk received his PhD degree (cum laude) in Systems and Control from the University of Groningen in 2020 and was awarded with the 2020 DISC Best PhD Thesis. During his PhD he was a visiting researcher at University of Washington, Seattle, in the lab of Mehran Mesbahi. After that he was a postdoctoral researcher, first at Cambridge University under supervision of Rodolphe Sepulchre, and later at ETH Zürich where he worked with Florian Dörfler. His research interests are in data-driven modeling and control as well as applications to networked systems and neuronal dynamics.
Title: \gamma-Conformance: A notion of system comparison
Abstract: Towards the development of a contract-based design framework, a crucial step is to conceive a notion of system comparison which affords one the chance to compare the input-output behavior of two systems in general, and a system and its specification in particular. Inspired by such theories as optimal H_∞ control and dissipativity, we propose a notion of system comparison measuring to what extent two systems behave similarly, in an input-output sense. More specifically, comparing two “non-deterministic” systems, this notion studies the condition where one system reveals an input-output behavior close to that of the other. More importantly, we equip our notion with an algebraic necessary and sufficient condition which can be verified easily. In particular, we show that such a condition can be formulated as an LMI, for which efficient and reliable computational tools are available.
The colloquium will take place online in Google Meet. You can email the organizer for a link to the meeting.
Title: A solution theory for coupled systems of PDEs and switched DAEs
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.
The colloquium will take place online in Google Meet. You can email the organizer for a link to the meeting.
Title: Clustering-based model reduction of network systems containing cycle
Abstract: In the model reduction of networked systems, clustering-based methods are able to preserve the network structure and synchronisation properties. However, the selection of clustering that results in a reduced-order model with optimal approximation error remains an open problem. The method of [1] enables identifying two nodes/sub-systems that show similar behaviour and, therefore, choosing two nodes to be clustered and resulting in a good approximation, based on the analysis of the Gramians of the edge dynamics. This method works perfectly on networked systems with tree structures, but the extension to more general graph structures containing cycles is not straightforward. In this colloquium, I will present my ongoing research on solving the problem of finding the best-clustering of networks containing cycles using the concept of Gramians for semi-stable systems [2].
[1] Besselink, Bart, Henrik Sandberg, and Karl H. Johansson. “Clustering-based model reduction of networked passive systems.” IEEE Transactions on Automatic Control 61.10 (2015): 2958-2973.
[2] Cheng, Xiaodong, and Jacquelien MA Scherpen. “Novel Gramians for linear semistable systems.” Automatica 115 (2020): 108911.
Title: Nonlinear (switched) DAEs: normal forms, impulse-free jumps and stability
Abstract: In the first part of this talk, we deal with inconsistent initial value problems of nonlinear DAEs of the form $E(x)\dot x= F(x)$. We define impulse-free jumps of nonlinear DAEs as parameterized curves with derivatives in the distribution $\ker E(x)$. Then with the help of a proposed nonlinear Weierstrass form, we study the existence and uniqueness of the impulse-free jumps. After that, a singular perturbed system approximation is proposed for nonlinear DAEs; we show that solutions of the perturbed system approximate both impulse-free jumps and $\mathcal C^1$-solutions of nonlinear DAEs. In the second part of the talk, we extend the jump rule in the first part to the switched case, which generalizes the impulse-free condition of switched linear DAEs to the nonlinear case. Moreover, a novel notion called the jump-flow explicitation is used to simply the common Lyapunov function condition for the stability analysis of switched nonlinear DAEs. Finally, we generalize the well-known commutativity condition of switched nonlinear ODEs to the DAEs case. We show that to guarantee the stability of nonlinear switched DAEs with all stable models, not only the commutativity of the flow vector fields but also some extra invariant conditions are needed.
Practice session for the CDC.
Title 1: Robustness of the Terminal Behaviour of Resistive Electrical Networks (Anne-Men)
Title 2: Behavioural Assume-Guarantee Contracts for Linear Dynamical Systems (Brayan)
Title 3: Observability and Determinability Characterizations for Switched Linear Systems in Discrete Time (Sutrisno)
