Tracking control for a class of random Lagrange systems with colored noise

For a class of Lagrange systems with colored noise, the problem of tracking control is considered. Using the structural properties of Lagrange systems, a Lyapunov function is skillfully constructed. Based on it, using backstepping idea, a 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. By a stochastic mechanical model, the reasonability of assumption is verified, and the simulation result demonstrates the effectiveness of the control scheme.