Research ArticleFinite time control for MIMO nonlinear system based on higher-order sliding mode

- Finite time control for MIMO system with high relative degree is achieved.
- Sliding mode chattering is greatly diminished by super-twisting algorithm.
- One can arbitrarily speed up the finite time transient process.
- Hovercraft trajectory tracking performances are enhanced.

Considering a class of MIMO uncertain nonlinear system, a novel finite time stable control algorithm is proposed based on higher-order sliding mode concept. The higher-order sliding mode control problem of MIMO nonlinear system is firstly transformed into finite time stability problem of multivariable system. Then continuous control law, which can guarantee finite time stabilization of nominal integral chain system, is employed. The second-order sliding mode is used to overcome the system uncertainties. High frequency chattering phenomenon of sliding mode is greatly weakened, and the arbitrarily fast convergence is reached. The finite time stability is proved based on the quadratic form Lyapunov function. Examples concerning the triple integral chain system with uncertainty and the hovercraft trajectory tracking are simulated respectively to verify the effectiveness and the robustness of the proposed algorithm.