Design of observers with gain adaptation for systems with disturbances: An orbital symmetry-based approach

We propose a framework for designing global observers for nonlinear systems with disturbances under geometric conditions based on orbital symmetries. Under some additional restrictions these orbital symmetry-based conditions boil down to geometric homogeneity (at infinity) conditions. Our observers are the result of the combination of a first filter, a state norm estimator, with a second filter adaptively tuned by the first and when compared with the existing literature have a completely novel structure, inherited by the orbital symmetry-based conditions. The observers exploit the geometric properties of orbital symmetries which are one-parameter groups of transformations capable of mapping the system state into neighbourhoods with parametrized width.