Global robust finite time control for a class of uncertain second-order nonlinear systems

For the tracking control of a class of uncertain second order nonlinear systems, this paper proposes a robust global finite time control strategy. This control strategy consists of two parts: firstly, a time-varying sliding mode controller is designed to make the tracking errors to zero at a desired finite time t_r; then, in the succeeding time t > t_r, another nonsingular terminal sliding mode controller is used to make the tracking errors stay at zero. The algorithm has the following advantages: 1) the tracking error convergence time can be set in advance; 2) error convergence rate can be adjusted by changing the value of a parameter; 3) global robustness is guaranteed for parameter uncertainty and external disturbance. Numerical results demonstrate the usefulness of the proposed control strategy.