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)
In view of the current research activities within the group Systems, Control and Applied Analysis (SCAA) and the joining of Prof. Juan Peypouquet as full professor in optimization, the group requested a name change to “Systems, Control and Optimization (SCO)” which was now granted by the FSE Faculty Board.
Kanat Camlibel from the SCAA group was recently promoted to Full Professor in recognition of his achievements in research, teaching and administration.
Title: A non-linear model for the water hammer problem
Abstract: The water flow and water hammer in a pipe is usually modelled by Euler equations which consists of 2 partial differential equations. The classical PDEs are nonlinear and inhomogeneous, and according to the existing research so far, it can be simplified to a switched DAE or ODE system under some assumptions. The result in some literature shows that simplification works well and converges to the PDE model by numerical solutions. However, how they (PDE and ODE model) converge to each other in an analytical way, or the error between them has not been quantified, and my work is to close this gap. The main method is to divide the process into 3 parts: before the valve closes, when the valve closes and after the valve has been closed.
The colloquium will take place online in Google Meet. You can email the organizer for a link to the meeting.
Title: Analytic Properties of Heat Equation Solutions and Reachable Sets
Abstract: We consider heat equations on bounded Lipschitz domains Omega in R^d and show that solutions to the heat equation for positive times are analytically extendable to a subdomain of the complex plane containing Omega. Our analysis is based on the boundary layer potential method for the heat equation. In particular, our method gives an explanation for the shapes appearing in the literature in 1d, which is not so easy to explain using Fourier analysis alone. I will also discuss the converse theorem, namely that certain sets in the complex plane can be realized as solutions to the heat equation on the boundary of Omega when Omega is a ball. Boundary layer potential theory also gives an indication that this statement is more difficult if Omega is not a ball. This exciting new technique to analyze the question of reachable sets is joint work with Alexander Strohmaier.
The colloquium will take place online in Google Meet. You can email the organizer for a link to the meeting.
Title: A contract theory for linear systems
Abstract: We introduce contracts for linear time-invariant systems with inputs and outputs. Contracts are used to express formal specifications on the dynamic behaviour of such systems through two aspects: assumptions and guarantees. The assumptions capture the available knowledge about the dynamic behaviour of the environment in which the system is supposed to operate. The guarantees capture the required dynamic behaviour of the system when interconnected with its environment. We also define and characterize notions of contract refinement and contract conjunction. The former allows one to compare contracts and the latter allows one to fuse the specifications expressed by multiple contracts. Finally, we also define and characterize notions of contract composition, which can be used to analyse and design interconnections of systems.
The colloquium will take place online in Google Meet. You can email the organizer for a link to the meeting.
This talk has been cancelled.
This talk has been cancelled.
Title: On Duality for Lyapunov Functions of Nonstrict Convex Processes
Abstract: This talk introduces a novel definition of Lyapunov functions for difference inclusions defined by convex processes. This class of systems is particularly interesting due to its application in modeling linear systems with conic (e.g. nonnegativity) constraints. After introducing the notions of weak and strong Lyapunov functions we will present a theorem revealing a duality relation between them. This relation will relate in a natural way to the duality between (strong) stabilizability and (strong) detectability of linear systems.
