Output Feedback Control of Inhomogeneous Parabolic PDEs with Point Actuation and Point Measurement using SOS and Semi-Separable Kernels

2015/03/24 by Aditya Gahlawat, Gahlawat, Aditya, Matthew M. Peet +1 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #FOS: Electrical engineering #Model Reduction and Neural Networks #Numerical methods for differential equations #Stability and Controllability of Differential Equations #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.1503.06982

openalex publication_date 2015/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we use SOS and SDP to design output feedback controllers for a class of one-dimensional parabolic partial differential equations with point measurements and point actuation. Our approach is based on the use of SOS to search for positive quadratic Lyapunov functions, controllers and observers. These Lyapunov functions, controllers and observers are parameterized by linear operators which are defined by SOS polynomials. The main result of the paper is the development of an improved class of observer-based controllers and evidence which indicates that when the system is controllable and observable, these methods will find a observer-based controller for sufficiently high polynomial degree (similar to well-known results from backstepping).

Cited by

• A New State-Space Representation of Lyapunov Stability for Coupled PDEs and Scalable Stability Analysis in the SOS Framework - with Lemma Proofs

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