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Sliding Mode Observer Design for a Parabolic PDE in the Presence of Unknown Inputs
Author(s) -
Orlov Yury,
Chakrabarty Sohom,
Zhao Dongya,
Spurgeon Sarah K.
Publication year - 2019
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1849
Subject(s) - mathematics , discretization , partial differential equation , ordinary differential equation , observer (physics) , ode , parabolic partial differential equation , control theory (sociology) , invariant (physics) , linear system , differential equation , mathematical analysis , computer science , control (management) , physics , quantum mechanics , artificial intelligence , mathematical physics
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.