Local sliding mode inversion algorithms and state observers with space applications

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.