An orbital symmetry-based approach to observer design for systems with disturbances

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 second filter adaptively exploits the properties of orbital symmetries of the system to achieve global convergence properties by steering, first, the state estimate close to the state trajectory and acting locally afterwards.