Local sliding mode inversion algorithms and state observers with space applications

Abstract

The main objective of this work is to propose novel finite‐time algorithms to either invert a time‐varying map or to estimate the state of a time‐varying nonlinear plant. The former goal is pursued by using a sliding mode version of the Newton algorithm, whereas the latter objective is achieved by resorting to the inverse of the Jacobian matrix of the observability map to implement a sliding mode differentiator in the original coordinates. Finally, it is shown how these two techniques can be efficiently used to solve some relevant space applications, such as the estimation of the angular velocity of an axial symmetric satellite, the estimation of the inertia parameters of an orbiting object from measurements of its angular velocities, and the estimation of a Keplerian orbital element given measurements of the other five ones.

Editorial: Sliding‐mode algorithms for state estimation and fault diagnosis

“…Possieri and Novara 10 propose a finite–time algorithm for either inverting a time–varying map or estimating the state of a time–varying nonlinear plant. The observer synthesis relies on sliding–mode differentiators.…”

Synthesis of Fractional Order Fuzzy Observer for a Fractional Order Takagi-Sugeno Model With Unmeasurable Premise Variables

“…Several methodologies have been proposed to alleviate chattering, albeit at the cost of permitting non-zero estimation errors. However, adopting this strategy entails a structural assumption concerning the nonlinear function, imposing a significant constraint in numerous scenarios [19,25].…”