State reconstruction of elastic systems using moving sensors

An alternate to the use of multiple sensing devices for an effective state estimation of spatially distributed systems is the use of a reduced number of scanning or scheduled ones. Earlier works considered the use of mobile sensors for the improved estimation of first order (parabolic) distributed parameter systems. This work considers the implementation of a moving sensor for the improved estimation of elastic systems and in particular systems governed by the one-dimensional wave (string) partial differential equation. The proposed state estimator is an application of a natural second order observer that uses a collocated filter gain that depends on the current position of the velocity sensor. The guidance of the moving sensor is extracted through the use of a parameter-dependent Lyapunov function that includes the kinetic and potential energy of the elastic system. The resulting guidance laws solely depend on the state estimation error and steer the mobile sensor to the spatial regions with larger estimation errors. Extensions to the guidance laws that take into account the motion dynamics of a mobile sensor are also presented. Extensive numerical studies examine the feasibility of using a mobile sensor for the improved state estimation of second order partial differential equations representing elastic systems.