Busca extremal para a PDE de Stefan com Fronteira Móvel

Abstract

This paper presents the design and analysis of the extremum seeking for static 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 differential equation (ODE). This is the first effort to pursue an extension of extremum seeking from the heat PDE to the Stefan PDE. We compensate the average-based actuation dynamics by a 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 convergence to a small neighborhood of the optimal point is proven by means of backstepping methodology, Lyapunov functional and averaging in infinite dimensions.