2019/03/25 by Iasson Karafyllis, Miroslav Krstić, Karafyllis, Iasson +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Electrical engineering #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Numerical methods for differential equations #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1903.10449
openalex publication_date 2019/03/25 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
This paper provides global exponential stabilization results by means of\nboundary feedback control for 1-D nonlinear unstable reaction-diffusion Partial\nDifferential Equations (PDEs) with nonlinearities of superlinear growth. The\nclass of systems studied are parabolic PDEs with nonlinear reaction terms that\nprovide "damping" when the norm of the state is large (the class includes\nreaction-diffusion PDEs with polynomial nonlinearities). The case of Dirichlet\nactuation at one end of the domain is considered and a Control-Lypunov\nFunctional construction is applied in conjunction with Stampacchia's truncation\nmethod. The paper also provides several important auxiliary results; among\nwhich is an extension of Wirtinger's inequality, used here for the construction\nof the Control Lyapunov functional.\n