多输入多输出非线性不确定系统连续高阶滑模控制

针对一类MIMO非线性不确定系统,提出一种新的连续高阶滑模控制算法.引入状态反馈使得系统高阶滑模控制问题等效转换为多变量不确定积分链的有限时间稳定问题,首先针对标称系统设计有限时间到达连续控制律,实现系统状态快速收敛,然后采用多变量非解耦形式超螺旋算法克服系统不确定性,实现鲁棒性,最终使得系统控制作用连续、滑模抖振得以大大抑制.基于二次型Lyapunov函数证明系统的有限时间稳定性.针对三阶不确定系统有限时间稳定和气垫船圆形航迹跟踪问题分别进行了仿真,验证了所提算法的有效性、鲁棒性.

Continuous higher-order sliding mode control for multi-input multi-output nonlinear uncertain system

This paper proposes a new continuous higher-order sliding mode control scheme for a class of MIMO nonlinearuncertain system. After implemented state feedback control, higher-order sliding mode control problem of the originaluncertain nonlinear system is equivalently transformed into finite time stability problem of multivariable uncertain integrorchains. A finite time continuous control law is firstly employed to guarantee rapid convergence of system states and finitetime stabilization of nominal integral chain system, then multivariable non-coupling super-twisting algorithm is designed toovercome system uncertainties and achieve robustness. Finally, the whole control effect is continuous and high frequencychattering phenomenon of sliding mode is greatly weakened. Finite time stability of the closed loop system is proved strictlybased on quadratic Lyapunov function. Examples concerning finite-time stabilization of a third order uncertain systemand the hovercraft circular trajectory tracking are simulated respectively to verify the effectiveness and the robustness ofthe proposed approach.