Input optimization for Observability of State Affine Systems
Résumé
In this paper a method for designing the input of a state affine system in order to guarantee a pre-specified degree of observability is proposed. It consists of an off-line algorithm to build an optimal, and so-called regularly persistent, input for the system. Optimality is defined with respect to the minimization of the input energy, and observability through a lower bound for the observability Gramian of the system, which is known to allow for an exponential observer design. The approach is presented for discrete-time systems, and is illustrated in simulation by an application example corresponding to a problem of fault detection in pipelines.