Output feedback tracking control of stochastic Lagrangian systems and its application

This paper focuses on the problem of output feedback tracking control for stochastic Lagrangian systems with the unmeasurable velocity. Under some milder assumptions, using the structural properties of Lagrangian systems, a reduced-order observer is skillfully constructed to estimate the velocity. Based on the observer, an output feedback tracking controller is designed such that the mean square of the tracking error converges to an arbitrarily small neighborhood of zero by tuning design parameters. The efficiency of the controller is demonstrated by a stochastic mechanical model.