一类控制系数未知但等同高阶非线性系统的稳定控制设计

Stabilizing Control Design for a Class of High-order Nonlinear Systems with Unknown but Identical Control Coefficients

本文研究了一类控制系数未知但等同高阶非线性系统的状态反馈稳定控制设计问题．尽管该类系统具有不确定性,即控制系数未知,但本文没有采用自适应技术,而是通过选取适当的设计参数,从而得到了设计该类非线性系统稳定控制器的新方法,并基于反推技术,给出了稳定控制器的设计步骤．所设计的状态反馈控制器使得闭环系统全局渐近稳定,并保持在原点的平衡性．

In this paper, the state-feedback stabilizing control design is investigated for a class of high-order nonlinear systems with unknown but identical control coefficients. Although there are system uncertainties, i.e., the unknown control coefficients, no adaptive technique but appropriately choosing design parameters is available in control design. Here a new approach is put forward to achieve a stabilizing controller for such a class of nonlinear systems. Using the backstepping approach, the design procedure for the stabilizing controller is presented. The designed state-feedback controller preserves the equilibrium at the origin, and guarantees that the closed-loop systems be globally asymptotically stable.