Backstepping Control For Lagrange Systems Disturbed By Colored Noise And Their Application

In this thesis,the problem of a class of lagrange system with colored noise is considered.First,by using the Lagrangian law,the mechanical system without disturbance is constructed.According to the dynamic-static method and relative motion principle,stochastic oscillations of surroundings are transformed into the disturbance on the controller,and then a lagrange system with colored noise is designed.The special structure of the quasi lower triangle of the system motivates us pay more attention to find a vectorial Backstepping controller.By selecting an appropriate Lyapunov-like function,a controller with tunable parameters is designed such that all signals of the closed-loop system are bounded and the track error can be made arbitrarily small.At last,this kind of method is applied to a random benchmark system,as a result that the system is noise to state exponential stability in 2-th moment(NSES-2-M)and the tracking error can be made arbitrarily small.By using simulation experience,the reasonability of the controller is verified.