Sliding Mode Observer Design for a Parabolic PDE in the Presence of Unknown Inputs

Abstract

This paper considers observer design for systems modeled by linear partial differential equations (PDEs) of parabolic type, which may be subject to unknown inputs. The system is assumed to have only one spatial dimension, over which it is discretised to obtain what is referred to as the lattice system, which is a set of linear time invariant (LTI) ordinary differential equations (ODEs) having a canonical Toeplitz-like structure with a specific sparsity pattern. This lattice structure is shown to be particularly appropriate for step-by-step sliding mode observer design that can reconstruct the state estimates at the points of discretisation and estimate the unknown input. Simulation results for both stable and unstable PDEs show that accurate state estimates can be provided at the points of discretisation. An approach to reconstruct the unknown input is demonstrated. © 2018 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd