Tracking controller design for random nonlinear TORA system

This paper considers a TORA system consists of a rolling ball and a moving car in the oscillating surroundings. By using the Lagrangian law, the dynamic model without disturbance is constructed. According to the relative motion principle, stochastic oscillations of surroundings are transformed into the random noises in the constructed Lagrange equation. The special structure of the quasi lower triangle of Lagrange equation motivates us pay more attentions to find a vectorial backstepping controller. By selecting an appropriate Lyapunov-like function, a backstepping controller with tunable parameters is designed such that all signals of the closed-loop system are bounded and track error can be made arbitrarily small.