A set-theoretic approach to observability and its application to process control. (August 2019) - López, Esteban; Gómez, Lina M.; Alvarez, Hernán
Highlights: The proposed quantification of observability depends on the measurement uncertainty and has a direct interpretation in terms of state estimation. In the absence of state estimation error, the devised controller guarantees convergence to the reference in a finite, predefined number of steps. State estimation accuracy is enhanced by employing the proposed observability-oriented controller. Control performance is not necessarily sacrificed to improve state estimation accuracy. Abstract: In this paper, a new approach to the observability of dynamical systems with uncertain sensors is developed. This approach is based on the redefinition of indistinguishability to consider measurement uncertainty and on the definition of a set called the final indiscernible set, which is directly related to state estimation accuracy and whose size is a quantitative observability index. Making use of this index, an observability-oriented controller, which attempts to drive the system through a high-observability trajectory to reduce estimation error, is proposed. Finally, this controller is illustrated through its application to the model of a CSTR, showing that the proposed method enhances the accuracy of state estimation when compared with a similar control scheme that does not consider observability and with a another kind of controller that employs a different observability index.