NONLINEAR VIRTUAL SENSORS DESIGN FROM DATA

The standard approach for observers design is to identify a model and then define an observer/Kalman filter based on the identified model. In general, nonlinear observer/Kalman filters are difficult to derive and/or to implement, and widely used solutions such as extended Kalman Filter approximations often exhibit poor performance, and even do not guarantee boundedness of the estimation error. In this paper, the idea of directly identifying a nonlinear observer from data is proposed. Such an idea can be applied when the sensor measuring the variable to be recovered fails or when a sensor is too complex and costly to be used, except for an initial set of experiments. The identified observer represents a “virtual” sensor which can be used when the “actual” sensor is no longer available. The approach proposed in this paper makes use of Set Membership methods recently developed for nonlinear systems. In case that the variable to be estimated is observable from the input-output signals, an almost optimal (in a worst case sense) virtual sensor is derived. Moreover, conditions are given for deriving a virtual sensor with bounded estimation error in the case that the variable to be estimated is not observable from the input-output signals. An example related to the Lorenz attractor is presented to demonstrate the effectiveness of the proposed approach.