含模型不确定性的上三角非线性系统的全局镇定

Global stabilization of upper-triangular nonlinear systems with model uncertainties

中文关键词  非线性系统  模型不确定性  嵌套饱和方法  鲁棒性  全局镇定

英文关键词  nonlinear system  model uncertainty  nested saturation approach  robustness  global stabilization

中文摘要

      本文针对一类具有模型不确定性的上三角非线性系统, 利用嵌套饱和函数方法研究其全局镇定问题. 首先, 对系统中存在的未知幂指数、未知控制参数和不确定性非线性函数施加适当假设, 并基于Lyapunov稳定性定理利 用已知的参数设计局部镇定控制器. 然后, 将设计的控制器与饱和函数结合得到饱和控制器. 通过适当选取饱和度, 可以证明只要不确定参数在限定的范围内, 该控制器都能够使得闭环系统全局渐近稳定. 最后, 选取不同的系统幂 指数搭建数值仿真算例. 在相同的控制器作用下, 系统状态和控制轨迹渐近收敛至原点, 从而验证了所提控制算法 的有效性和鲁棒性.

英文摘要

      Based on the nested-saturation method, this paper considers the global stabilization problem for a class of upper-triangular nonlinear systems with model uncertainties. First, with respect to the unknown power integrators, control coefficients and uncertain nonlinear functions, certain assumptions are imposed. According to the Lyapunov stability theory, a state-feedback controller, only involving the known parameters, is iteratively designed to locally stabilize the nonlinear system. Then, a saturated controller is constructed by combining the nested function and the local stabilizer. With appropriately chosen saturation level, it can be proved that the saturated controller is able to make the closed-loop system globally asymptotically stable as long as the uncertain terms stay within the specified limits. Finally, a simulation example is conducted by selecting different sets of power integrators. With the same controller, system state and control trajectories converge to the origin asymptotically, which indicates the effectiveness and robustness of the proposed control scheme.