Busca extremal para equações diferenciais parciais de Stefan com fronteira móvel

Abstract

This dissertation presents the design and analysis of the extremum seeking for sta- tic maps with input governed by a parabolic partial differential equation (PDE) of the

diffusion type defined on a time varying spatial domain described by an ordinary differen- tial equation (ODE). This is the first effort to pursue an extension of extremum seeking

from the heat PDE to the Stefan PDE. The compensation of the average-based actua- tion dynamics is performed by a backstepping controller via backstepping transformation

for the moving boundary, which is utilized to transform the original coupled PDE-ODE

into a target system whose exponential stability is proved. The local exponential conver- gence to a small neighborhood of the optimal point is proven by means of backstepping

methodology, Lyapunov-Krasovskii functional and averaging in infinite dimensions. The extension for the delay-compensated extremum seeking control of the Stefan problem is also discussed.