Backstepping observer using weighted spatial average for 1-dimensional parabolic distributed parameter systems

摘要

This paper is concerned with designing a backstepping-based observer for a class of 1-dimensional parabolic distributed parameter systems whose output is a weighted spatial average of the state. We first show that an integral transformation converts the original system into another parabolic system with boundary observation if the weighting function satisfies a parameterized ordinary differential equation. Then the backstepping observer for the transformed system is available and an estimate of the original state is obtained through the inverse transformation. We also show that the estimation error exponentially converges to 0 in terms of the L~2 norm with arbitrary decay rate. Furthermore, a closed-form expression of the observer is provided for systems described by linear reaction-diffusion equations.