Modeling and adaptive tracking for a class of stochastic Lagrangian control systems

This paper focuses on the problem of modeling and adaptive tracking for a class of stochastic Lagrangian control systems with unknown parameters. By reasonably introducing random noise, a method to construct stochastic Lagrangian control systems is given. Under some milder assumptions, an adaptive 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 reasonability of assumptions and the efficiency of the controller are demonstrated by a mechanics model in random vibration environment.