A practical observer for state and sensor fault reconstruction of a class of fractional‐order nonlinear systems

Practical observers have been widely used in the literature for the purpose of estimating states for integer-order disturbed and/or uncertain systems. However, much less research has been done to propose practical observers for fractional-order disturbed and/or uncertain systems. As for sensor fault estimation, and to the best of the authors’ knowledge, no previous works have developed an adaptive practical observer to address the problem. In this paper, the authors propose, for the first time, an adaptive practical observer to reconstruct simultaneously the states and sensor faults for Lipschitz fractional systems. Another merit of this work, is that the class of nonlinear systems, used here, is some kind of disturbed Lipschitz system. That is to say, the Lipschitz assumption here is a modified version of the classical Lipschitz condition. And this modified version has been newly introduced in the literature, in a recent article. To validate the developed theoretical results, a numerical example is studied in the final section.