Input Reconstruction by Feedback Control for the Schlögl and FitzHugh–Nagumo Equations

Abstract

Dynamical reconstruction of unknown time-varying controls from inexact measurements of the state function is investigated for a semilinear parabolic equation with memory. This system includes as particular cases the Schlögl model and the FitzHugh–Nagumo equations. A numerical method is suggested that is based on techniques of feedback control. An error analysis is performed. Numerical examples confirm the theoretical predictions.

Keywords

• semilinear parabolic equation
• input reconstruction