针对传统Backstepping动态面控制中滤波器跟踪误差及控制误差在靠近原点阶段收敛较慢、收敛时间无限大、控制器增益存在脆弱性等问题, 设计了适用于具有不确定和外干扰的高阶多输入多输出非线性系统的固定时间收敛动态面Backstepping控制。首先提出并证明一种新的固定时间收敛的李雅普诺夫定理;基于此结论, 将每一层子系统的虚拟控制器和滤波器均设计为固定时间收敛的新型结构。相对现有方案, 新方案的优点是:1) 加快了跟踪误差轨迹在远离和靠近平衡点两个阶段的收敛速度, 即全论域的快速化;2) 避免了参数脆弱性的问题;3) 跟踪误差和控制误差都是固定时间收敛的, 即不论初始误差多大, 收敛时间不仅有限而且存在与初始误差无关的固定上界;4) 虚拟控制器和控制器均为非奇异的。

The conventional dynamic surface of Backstepping control is designed as first order filter.Its drawbacks include slow converging speed of tracking/controlling error when closing to equilibrium point, infinite convergence time and vulnerability of the controller gain.In view of these problems, this paper proposes a novel fixed-time convergent Backstepping control scheme based on fixed-time convergent dynamic surface for higher-order multi-input-multi-output nonlinear systems with uncertainties and external disturbance.Firstly, a new fixed-time convergent Lyapunov theorem is proposed and proved.Based on this new tool, the virtual controller and filter of the subsystem of each level are designed with the fixed-time convergent structure.Compared with conventional schemes, the new scheme has the following advantages:1) Speeding up the convergence of tracking error at two stages of far from and closing to the equilibrium point, i.e., the convergence speed is improved within the whole universe;2) Overcoming the parameter vulnerability problem;3) Both the tracking error and controlling error are fixed-time convergent, which means that the convergent time is limited and a fixed upper-bound is existed no matter how big the initial error is;and 4) Both the virtual controller and the controller are nonsingular.