多输入多输出非线性不确定系统连续高阶滑模控制
Continuous higher-order sliding mode control for multi-input multi-output nonlinear uncertain system

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