State estimation and reconstruction of unknown inputs with arbitrary relative degree via a predefined-time algebraic solver

• Published in: Journal of the Franklin Institute 2020-09, Vol.357 (13), p.9083-9106
• Main Authors: López, Esteban, Botero, Héctor
• Format: Article
• Language: English
• Subjects: Algebra; Dynamical systems; Estimating techniques; Extended Kalman filter; Kalman filters; Nonlinear systems; Reconstruction; State estimation; State variable; State vectors
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2020.07.003

•Unknown inputs are estimated without imposing relative-degree-related conditions.•The scheme employs an original predefined-time stable algebraic solver.•Implementation does not require to apply a state transformation on the system.•The system does not need to be affine in the unknown inputs.•The proposed observer has been shown to outperform an extended Kalman–Bucy filter. This paper proposes a sliding mode observer for the estimation of the state variables and the reconstruction of the unknown inputs of nonlinear dynamical systems regardless of whether these systems satisfy relative-degree-related conditions or not. This observer is based on a predefined-time sliding mode algebraic solver and does not require the explicit use of state transformations. The use of the proposed method is illustrated through its application to an abstract system and the model of a chemical process, achieving an accurate estimation of both the state vector and the unknown inputs in each case, while an extended Kalman filter applied to the chemical process for comparison maintains significant estimation error.