R. Katz. Finite-dimensional observer-based ISS and $L^2$-gain control of parabolic PDEs
Talk at the Online Seminar "Input-to-State Stability and its Applications"
https://researchseminars.org/seminar/...
Speaker:
Rami Katz (Tel-Aviv University, Israel)
For slides and publication list: https://www.ramikatz.com/
Title:
Finite-dimensional observer-based ISS and $L^2$-gain control of parabolic PDEs
Abstract:
Finite-dimensional observer-based controller design for PDEs is a challenging problem. In this talk, construction of such controllers via the modal decomposition method for linear parabolic 1D PDEs will be presented. We will start with finite-dimensional observer-based control for the linear heat equation where at least one of the control or observation operators is bounded. We will proceed with the case of both operators unbounded, where dynamic extension is helpful. Here we will consider ISS and $L^2$-gain analysis of the Kuramoto-Sivashinsky equation. The extension of the results to time-varying input/output delays, as well as arbitrarily large constant input delays will be presented. Finally, we will discuss sampled-data implementation of finite-dimensional boundary controllers for the 1D heat equation under discrete-time point measurement, via a generalized hold device. An essential tool for the ISS analysis will be a novel ISS Halanay’s inequality with explicit constants in the bounds.
Joint work with Emilia Fridman
https://scholar.google.co.il/citation...
Date:
Thursday, 09 December 2021