Neuro-observer based on backstepping technique for distributed parameters systems

The aim of this manuscript is to present an observer design for partially known distributed parameters systems described by Partial Differential Equations (PDE) using Differential Neural Networks (DNN) methodology and backstepping-like procedure. A Volterra-like integral transformation is used to change the coordinates of the error dynamics into exponentially stable target system. This gives as a result the output injection functions of the observer which are obtained by solving a PDE system. DNN are used to find an explicit solution to the PDE system and to make the observer gains to be discontinuous which have well known advantages. Theoretical results were proved using the Lyapunov theory. A numerical example demonstrates the proposed method effectiveness.