Adaptive Pseudo-Inverse Observers for Output Redundant Discrete-Time Linear Systems

We address the problem of output redundancy in discrete-time linear systems, with the aim of obtaining an optimized combination of sensors for structurally rejecting certain disturbances. We frame our goal as the design problem of a nonlinear observer consisting in a linear Luenberger structure augmented with an adaptive weighted pseudo-inverse combination of the available measurements. A novel optimization algorithm is proposed for the update of the dynamic weights of the pseudo-inverse, together with a selector that overrides the optimizer whenever the pseudo-inverse becomes close to being singular. Numerical simulations on the case study of a discrete-time mechanical system support and validate the proposed architecture.