Online observability optimization for state affine systems with output injection and observer design

Observability being in general subject to the applied input for a nonlinear system, the aim of the present work is to propose an input selection strategy for a special class of systems, so as to make them observable. The considered systems are those admitting a state-affine structure with output injection. For such systems, an online algorithm is proposed to compute an appropriate input in real time. It guarantees observability by ensuring a lower bound on the related Gramian, and minimizes at the same time the input variations with respect to some reference value required for the system operation. This computation is updated at each time with the new output measurements becoming available. The proposed methodology is illustrated on a piping system example, for which an exponential observer is finally obtained.