Adaptive Pseudoinverse 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 pseudoinverse combination of the available measurements. A novel optimization algorithm is proposed for the update of the dynamic weights of the pseudoinverse, together with a selector that overrides the optimizer whenever the pseudoinverse becomes close to being singular. Numerical simulations on the case study of a discrete-time mechanical system support and validate the proposed architecture.